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Volumn 21, Issue , 2006, Pages 1-317

Functional approach to nonlinear models of water flow in soils

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EID: 84892106755     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/1-4020-4880-7     Document Type: Book
Times cited : (33)

References (134)
  • 1
    • 0000836987 scopus 로고
    • Quasi-linear elliptic-parabolic differential equations
    • H. W. Alt, S. Luckhaus: Quasi-linear elliptic-parabolic differential equations. Math. Z., 183, 311-341 (1983)
    • (1983) Math. Z. , vol.183 , pp. 311-341
    • Alt, H.W.1    Luckhaus, S.2
  • 4
    • 0001323666 scopus 로고
    • Un th́eor̀eme de compacit́e
    • J. P. Aubin: Un th́eor̀eme de compacit́e. C.R. Acad. Sci. Paris, Śerie I 256, 5042-5044 (1963)
    • (1963) C.R. Acad. Sci. Paris Śerie i , vol.256 , pp. 5042-5044
    • Aubin, J.P.1
  • 5
    • 0002293879 scopus 로고
    • The porous medium equation
    • (A. Fasano, M. Primicerio, eds.), Lecture Notes in Mathematics Springer, Berlin
    • D. G. Aronson: The porous medium equation. In: Some Problems in Nonlinear Diffusion (A. Fasano, M. Primicerio, eds.), Lecture Notes in Mathematics, 1224, Springer, Berlin 1986
    • (1986) Some Problems in Nonlinear Diffusion , vol.1224
    • Aronson, D.G.1
  • 7
    • 34248233495 scopus 로고    scopus 로고
    • Porous media filtration with hysteresis
    • F. Bagagiolo, A. Visintin: Porous media filtration with hysteresis. Adv. Math. Sci. Appl., 14, 379-403 (2004)
    • (2004) Adv. Math. Sci. Appl. , vol.14 , pp. 379-403
    • Bagagiolo, F.1    Visintin, A.2
  • 8
    • 0000894022 scopus 로고
    • Su un problema di frontiera libera conesso a questioni di idraulica
    • C. Baiocchi: Su un problema di frontiera libera conesso a questioni di idraulica. Ann. Mat. Pura Appl., 92, 107-127 (1972)
    • (1972) Ann. Mat. Pura Appl. , vol.92 , pp. 107-127
    • Baiocchi, C.1
  • 16
    • 10844257877 scopus 로고    scopus 로고
    • Controlling the volumetric water content jump in a stratified unsaturated soil
    • (A. Ravi, D. O'Regan, eds.) Kluwer Academic Publishers
    • V. Barbu, G. Marinoschi: Controlling the volumetric water content jump in a stratified unsaturated soil. In: Nonlinear Analysis and Applications, To V. Lakshmikantham on his 80th birthday (A. Ravi, D. O'Regan, eds.), 1, Kluwer Academic Publishers 2003, pp. 241-258
    • (2003) Nonlinear Analysis and Applications, to V. Lakshmikantham on His 80th Birthday , vol.1 , pp. 241-258
    • Barbu, V.1    Marinoschi, G.2
  • 17
    • 0142023986 scopus 로고    scopus 로고
    • Existence for a time dependent rainfall infiltration model with a blowing up diffusivity
    • V. Barbu, G. Marinoschi: Existence for a time dependent rainfall infiltration model with a blowing up diffusivity. Nonlinear Analysis Real World Applications, 5, 2, 231-245 (2004)
    • (2004) Nonlinear Analysis Real World Applications , vol.5 , Issue.2 , pp. 231-245
    • Barbu, V.1    Marinoschi, G.2
  • 21
    • 0039026205 scopus 로고
    • Introduction to modeling of transport phenomena in porous media
    • (J. Bear, ed.), Kluwer Academic Publishers
    • J. Bear, Y. Bachmat: Introduction to Modeling of Transport Phenomena in Porous Media. Theory and Applications of Transport in Porous Media. Volume 4, (J. Bear, ed.), Kluwer Academic Publishers 1991
    • (1991) Theory and Applications of Transport in Porous Media. , vol.4
    • Bear, J.1    Bachmat, Y.2
  • 22
    • 0037670870 scopus 로고    scopus 로고
    • Positive solutions of the porous medium equation with hysteresis
    • A. Beliaev: Positive solutions of the porous medium equation with hysteresis. J. Math. Anal. Appl., 281, 125-137 (2003)
    • (2003) J. Math. Anal. Appl. , vol.281 , pp. 125-137
    • Beliaev, A.1
  • 24
    • 0042376716 scopus 로고    scopus 로고
    • On a parabolic equation with slow and fast diffusion
    • P. Benilan, J. Bouillet: On a parabolic equation with slow and fast diffusion. Nonlinear Analysis TMA, 26, 4, 813-822 (1996)
    • (1996) Nonlinear Analysis TMA , vol.26 , Issue.4 , pp. 813-822
    • Benilan, P.1    Bouillet, J.2
  • 25
    • 21844491188 scopus 로고
    • Quasilinear first-order equations with continuous nonlinearities
    • P. Benilan, S. N. Krushkov: Quasilinear first-order equations with continuous nonlinearities. Russian Acad. Sci. Dokl. Math., 50, 3, 391-396 (1995)
    • (1995) Russian Acad. Sci. Dokl. Math. , vol.50 , Issue.3 , pp. 391-396
    • Benilan, P.1    Krushkov, S.N.2
  • 27
    • 4344603515 scopus 로고    scopus 로고
    • On the infiltration of rain water through the soil with runoff of the excess water
    • I. Borsi, A. Farina, A. Fasano: On the infiltration of rain water through the soil with runoff of the excess water. Nonlinear Analysis Real World Applications, 5, 763-800 (2004)
    • (2004) Nonlinear Analysis Real World Applications , vol.5 , pp. 763-800
    • Borsi, I.1    Farina, A.2    Fasano, A.3
  • 28
    • 0002239265 scopus 로고
    • Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations
    • (E. Zarantonello, ed.), Academic Press
    • H. Brezis: Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations. In: Contributions to Nonlinear Functional Analysis. (E. Zarantonello, ed.), Academic Press 1971
    • (1971) Contributions to Nonlinear Functional Analysis
    • Brezis, H.1
  • 29
    • 0001968839 scopus 로고
    • Probl̀emes unilat́eraux
    • H. Brezis: Probl̀emes unilat́eraux. J. Math. Pures Appl., 51, 1-164 (1972)
    • (1972) J. Math. Pures Appl. , vol.51 , pp. 1-164
    • Brezis, H.1
  • 32
    • 0023531108 scopus 로고
    • Time-to-ponding: Comparison of analytic, quasi-analytic and approximate predictions
    • P. Broadbridge, I. White: Time-to-ponding: Comparison of analytic, quasi-analytic and approximate predictions. Water Resources Research, 23, 12, 2302-2310 (1987)
    • (1987) Water Resources Research , vol.23 , Issue.12 , pp. 2302-2310
    • Broadbridge, P.1    White, I.2
  • 33
    • 0023823587 scopus 로고
    • Constant rate rainfall infiltration: A versatile nonlinear model. 1. Analytic solution
    • P. Broadbridge, I. White: Constant rate rainfall infiltration: A versatile nonlinear model. 1. Analytic solution. Water Resources Research, 24, 1, 145-154 (1988)
    • (1988) Water Resources Research , vol.24 , Issue.1 , pp. 145-154
    • Broadbridge, P.1    White, I.2
  • 34
    • 0024163225 scopus 로고
    • Constant rate rainfall in a bounded profile: Solutions of a nonlinear model
    • P. Broadbrigde, J. H. Knight, C. Rogers: Constant rate rainfall in a bounded profile: Solutions of a nonlinear model. Soil Sci. Soc. Am. J., 52, 1526-1533 (1988)
    • (1988) Soil Sci. Soc. Am. J. , vol.52 , pp. 1526-1533
    • Broadbrigde, P.1    Knight, J.H.2    Rogers, C.3
  • 36
    • 0037758074 scopus 로고
    • Nonlinear initial value problems
    • F. E. Browder: Nonlinear initial value problems. Ann. of Math., 82, 51-87 (1965)
    • (1965) Ann. of Math. , vol.82 , pp. 51-87
    • Browder, F.E.1
  • 37
    • 0040374231 scopus 로고
    • Existence and uniqueness theorems for solutions of nonlinear boundary value problems
    • A.M.S
    • F. E. Browder: Existence and uniqueness theorems for solutions of nonlinear boundary value problems. Symposia in Appl. Math., 17, A.M.S., 24-29 (1965)
    • (1965) Symposia in Appl. Math. , vol.17 , pp. 24-29
    • Browder, F.E.1
  • 38
    • 34250534713 scopus 로고
    • Nonlinear maximal monotone operators in Banach spaces
    • F. E. Browder: Nonlinear maximal monotone operators in Banach spaces. Math. Ann., 177, 283-301 (1968)
    • (1968) Math. Ann. , vol.177 , pp. 283-301
    • Browder, F.E.1
  • 39
    • 0001864855 scopus 로고
    • Studies on the movement of soil moisture
    • U.S. Gov. Print. Office, Washington, DC
    • E. Buckingham: Studies on the movement of soil moisture. USDA Bur. Soils Bull., 38, U.S. Gov. Print. Office, Washington, DC (1907)
    • (1907) USDA Bur. Soils Bull. , vol.38
    • Buckingham, E.1
  • 41
    • 0000945203 scopus 로고
    • Unicit́e des solutions du type Krushkov pour des problemes elliptique avec des termes de transport non lińeaires
    • J. Carillo: Unicit́e des solutions du type Krushkov pour des problemes elliptique avec des termes de transport non lińeaires. C. R. Acad. Sci. Paris, Serie I, 303, 189-192 (1986)
    • (1986) C. R. Acad. Sci. Paris Serie i , vol.303 , pp. 189-192
    • Carillo, J.1
  • 42
    • 38149144984 scopus 로고
    • On the uniqueness of the solution of the evolution dam problem
    • J. Carillo: On the uniqueness of the solution of the evolution dam problem. Nonlinear Analysis 22, 573-607 (1994)
    • (1994) Nonlinear Analysis , vol.22 , pp. 573-607
    • Carillo, J.1
  • 43
    • 0033407951 scopus 로고    scopus 로고
    • Entropy solutions for nonlinear degenerate problems
    • J. Carillo: Entropy solutions for nonlinear degenerate problems. Arch. Rational Mech. Anal., 147, 269-361 (1999)
    • (1999) Arch. Rational Mech. Anal. , vol.147 , pp. 269-361
    • Carillo, J.1
  • 44
    • 0033587465 scopus 로고    scopus 로고
    • Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems
    • J. Carillo, P. Wittbold: Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems. J. Differential Equations, 156, 93-121 (1999)
    • (1999) J. Differential Equations , vol.156 , pp. 93-121
    • Carillo, J.1    Wittbold, P.2
  • 46
    • 84990574706 scopus 로고
    • On singular diffusion equations with applications to self-organized criticality
    • J. T. Chayes, S. J. Osher, J. V. Ralston: On singular diffusion equations with applications to self-organized criticality. Comm. Pure Appl. Math., 46, 1363-1377 (1993)
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 1363-1377
    • Chayes, J.T.1    Osher, S.J.2    Ralston, J.V.3
  • 48
    • 0012684812 scopus 로고
    • Semi-groups of nonlinear contractions and dissipative sets
    • M. G. Crandall, A. Pazy: Semi-groups of nonlinear contractions and dissipative sets. J. Funct. Anal., 3, 376-418 (1969)
    • (1969) J. Funct. Anal. , vol.3 , pp. 376-418
    • Crandall, M.G.1    Pazy, A.2
  • 49
    • 51249191929 scopus 로고
    • Nonlinear evolution equations in Banach spaces
    • M. G. Crandall, A. Pazy: Nonlinear evolution equations in Banach spaces. Israel J. Math., 11, 57-94 (1972)
    • (1972) Israel J. Math. , vol.11 , pp. 57-94
    • Crandall, M.G.1    Pazy, A.2
  • 51
    • 0031351679 scopus 로고    scopus 로고
    • On nonlinear parabolic equations of very fast diffusion
    • P. Daskalopoulos, M. Del Pino: On nonlinear parabolic equations of very fast diffusion. Arch. Rational Mech. Anal., 137, 363-380 (1997)
    • (1997) Arch. Rational Mech. Anal. , vol.137 , pp. 363-380
    • Daskalopoulos, P.1    Del Pino, M.2
  • 52
    • 1842695585 scopus 로고
    • Wetting: Statics and dynamics
    • P. G. De Gennes: Wetting: statics and dynamics. Reviews of Modern Phys., 57, 827-863 (1985)
    • (1985) Reviews of Modern Phys. , vol.57 , pp. 827-863
    • De Gennes, P.G.1
  • 56
    • 0000558104 scopus 로고    scopus 로고
    • The fast diffusion equation with logarithmic nonlinearity and the evolution of conformal metrics in the plane
    • J. R. Esteban, A. Rodriguez, J. L. V́azquez: The fast diffusion equation with logarithmic nonlinearity and the evolution of conformal metrics in the plane. Adv. Differential Equations, 1, 21-50 (1996)
    • (1996) Adv. Differential Equations , vol.1 , pp. 21-50
    • Esteban, J.R.1    Rodriguez, A.2    V́azquez, J.L.3
  • 57
    • 0001420538 scopus 로고    scopus 로고
    • The maximal solution of the logarithmic fast diffusion equation in two space dimensions
    • J. R. Esteban, A. Rodriguez, J. L. V́azquez: The maximal solution of the logarithmic fast diffusion equation in two space dimensions. Adv. Differential Equations, 2, 867-894 (1997)
    • (1997) Adv. Differential Equations , vol.2 , pp. 867-894
    • Esteban, J.R.1    Rodriguez, A.2    V́azquez, J.L.3
  • 58
    • 0018544691 scopus 로고
    • Free boundary problems for nonlinear parabolic equations with nonlinear free bounadry conditions
    • A. Fasano, M. Primicerio: Free boundary problems for nonlinear parabolic equations with nonlinear free bounadry conditions. J. Math. Anal. Appl., 72, 247-273 (1979)
    • (1979) J. Math. Anal. Appl. , vol.72 , pp. 247-273
    • Fasano, A.1    Primicerio, M.2
  • 59
    • 33645125873 scopus 로고
    • Liquid flow in partially saturated porous media
    • A. Fasano, M. Primicerio: Liquid flow in partially saturated porous media. J. Inst. Math. Appl., 23, 503-517 (1979)
    • (1979) J. Inst. Math. Appl. , vol.23 , pp. 503-517
    • Fasano, A.1    Primicerio, M.2
  • 60
    • 1142271128 scopus 로고    scopus 로고
    • Approximation results for semigroups generated by multivalued linear operators and applications
    • A. Favini, M. Fuhrman: Approximation results for semigroups generated by multivalued linear operators and applications. Differential Integral Equations, 11, 5, 781-805 (1998)
    • (1998) Differential Integral Equations , vol.11 , Issue.5 , pp. 781-805
    • Favini, A.1    Fuhrman, M.2
  • 62
    • 4444318875 scopus 로고    scopus 로고
    • Quasilinear degenerate evolution equations in Banach spaces
    • A. Favini, A. Yagi: Quasilinear degenerate evolution equations in Banach spaces. J. Evolution Equations, 4, 421-449 (2004)
    • (2004) J. Evolution Equations , vol.4 , pp. 421-449
    • Favini, A.1    Yagi, A.2
  • 64
    • 0033445880 scopus 로고    scopus 로고
    • Modelling surface runoff and infiltration of rain by an elliptic-parabolic equation coupled with a first-order equation on the boundary
    • J. Filo, S. Luckhaus: Modelling surface runoff and infiltration of rain by an elliptic-parabolic equation coupled with a first-order equation on the boundary. Arch. Rational Mech. Anal., 146, 157-182 (1999)
    • (1999) Arch. Rational Mech. Anal. , vol.146 , pp. 157-182
    • Filo, J.1    Luckhaus, S.2
  • 65
    • 0000754923 scopus 로고
    • On the exactly solvable equation occuring in two-phase flow in porous media
    • A. S. Fokas, Y C. Yortsos: On the exactly solvable equation occuring in two-phase flow in porous media. SIAM J. Appl. Math., 42, 318-332 (1982)
    • (1982) SIAM J. Appl. Math. , vol.42 , pp. 318-332
    • Fokas, A.S.1    Yortsos, Y.C.2
  • 66
    • 4344655612 scopus 로고
    • A filtration problem with ponding
    • R. Gianni: A filtration problem with ponding. Boll. Un. Mat. Ital., 5 B, 875-891 (1991)
    • (1991) Boll. Un. Mat. Ital. , vol.5 B , pp. 875-891
    • Gianni, R.1
  • 67
    • 84973050689 scopus 로고
    • A new approach to evolution free boundary problems
    • G. Gilardi: A new approach to evolution free boundary problems. Comm. Partial Differential Equations, 4, 1099-1122 (1979)
    • (1979) Comm. Partial Differential Equations , vol.4 , pp. 1099-1122
    • Gilardi, G.1
  • 70
    • 1042263479 scopus 로고    scopus 로고
    • On some Dirichlet and Cauchy problems for a singular diffusion equation
    • K. M. Hui: On some Dirichlet and Cauchy problems for a singular diffusion equation. Differential Integral Equations. 15, 7, 769-804 (2002)
    • (2002) Differential Integral Equations. , vol.15 , Issue.7 , pp. 769-804
    • Hui, K.M.1
  • 71
    • 0344272637 scopus 로고    scopus 로고
    • Asymptotic behaviour of solutions of the equation ut =Δ log u near the extinction time
    • S. Y. Hsu: Asymptotic behaviour of solutions of the equation ut =Δ log u near the extinction time. Adv. Differential Equations, 8, 2, 161-187 (2003)
    • (2003) Adv. Differential Equations , vol.8 , Issue.2 , pp. 161-187
    • Hsu, S.Y.1
  • 72
    • 0345135039 scopus 로고    scopus 로고
    • Uniqueness of solutions of a singular diffusion equation
    • S. Y. Hsu: Uniqueness of solutions of a singular diffusion equation. Differential Integral Equations, 16, 2, 181-200 (2003)
    • (2003) Differential Integral Equations , vol.16 , Issue.2 , pp. 181-200
    • Hsu, S.Y.1
  • 73
    • 0002970598 scopus 로고    scopus 로고
    • Numerical identification of parameters in parabolic systems
    • Y. L. Keung, J. Zou: Numerical identification of parameters in parabolic systems. Inverse Problems, 14, 83-100 (1998)
    • (1998) Inverse Problems , vol.14 , pp. 83-100
    • Keung, Y.L.1    Zou, J.2
  • 74
    • 84934736228 scopus 로고
    • Exact solutions in nonlinear diffusion
    • J. H. Knight J. H, J. R. Philip: Exact solutions in nonlinear diffusion. J. Engrg. Math., 8, 219-227 (1974)
    • (1974) J. Engrg. Math. , vol.8 , pp. 219-227
    • Knight J H, J.H.1    Philip, J.R.2
  • 75
    • 0013561556 scopus 로고
    • On solving the unsaturated flow equation: 2. Critique of Parlange's method
    • J. H. Knight, J. R. Philip: On solving the unsaturated flow equation: 2. Critique of Parlange's method. Soil Sci., 116, 6, 407-416 (1974)
    • (1974) Soil Sci. , vol.116 , Issue.6 , pp. 407-416
    • Knight, J.H.1    Philip, J.R.2
  • 76
    • 84972544461 scopus 로고
    • Nonlinear semi-groups in Hilbert spaces
    • Y. Komura: Nonlinear semi-groups in Hilbert spaces. J. Math. Soc. Japan, 19, 493-507 (1967)
    • (1967) J. Math. Soc. Japan , vol.19 , pp. 493-507
    • Komura, Y.1
  • 79
    • 0000604204 scopus 로고
    • Generalized solutions of the Cauchy problem in the large for first-order nonlinear equations
    • S. N. Krushkov: Generalized solutions of the Cauchy problem in the large for first-order nonlinear equations. Soviet Math. Dokl., 10, 785-788 (1969)
    • (1969) Soviet Math. Dokl. , vol.10 , pp. 785-788
    • Krushkov, S.N.1
  • 80
    • 2942655353 scopus 로고    scopus 로고
    • A filtration model with hysteresis
    • M. Kubo: A filtration model with hysteresis. J. Differential Equations, 201, 75-98 (2004)
    • (2004) J. Differential Equations , vol.201 , pp. 75-98
    • Kubo, M.1
  • 81
    • 0003715566 scopus 로고    scopus 로고
    • Control theory for partial differential equations: Continuous and approximation theories I: Abstract parabolic systems
    • Cambridge University Press
    • I. Lasiecka, R. Triggiani: Control Theory for Partial Differential Equations: Continuous and Approximation Theories I: Abstract Parabolic Systems. Encyclopedia of mathematics and its applications series, Cambridge University Press 2000
    • (2000) Encyclopedia of Mathematics and Its Applications Series
    • Lasiecka, I.1    Triggiani, R.2
  • 85
    • 0142078131 scopus 로고    scopus 로고
    • Nonlinear infiltration with a singular diffusion coefficient
    • G. Marinoschi: Nonlinear infiltration with a singular diffusion coefficient. Differential Integral Equations, 16, 9, 1093-1110 (2003)
    • (2003) Differential Integral Equations , vol.16 , Issue.9 , pp. 1093-1110
    • Marinoschi, G.1
  • 86
    • 84892053347 scopus 로고    scopus 로고
    • On some problems concerning the nonlinear infiltration in un-saturated media
    • Alushta, Ukraine, September 2003 (to appear)
    • G. Marinoschi: On some problems concerning the nonlinear infiltration in un-saturated media. Proceedings of the International Conference NPDE 2003", Alushta, Ukraine, September 2003 (to appear)
    • Proceedings of the International Conference NPDE 2003"
    • Marinoschi, G.1
  • 87
    • 10844239004 scopus 로고    scopus 로고
    • A free boundary problem describing the saturated unsaturated flow in a porous medium
    • G. Marinoschi: A free boundary problem describing the saturated unsaturated flow in a porous medium. Abstr. Appl. Anal., 2004:9, 729-755 (2004)
    • (2004) Abstr. Appl. Anal. , vol.2004 , Issue.9 , pp. 729-755
    • Marinoschi, G.1
  • 88
    • 33645786905 scopus 로고    scopus 로고
    • A free boundary problem describing the saturated unsaturated flow in a porous medium. II. Existence of the free boundary in the 3-D case
    • G. Marinoschi: A free boundary problem describing the saturated unsaturated flow in a porous medium. II. Existence of the free boundary in the 3-D case. Abstr. Appl. Anal., 2005:8, 813-854 (2005)
    • (2005) Abstr. Appl. Anal. , vol.2005 , Issue.8 , pp. 813-854
    • Marinoschi, G.1
  • 90
    • 84892121566 scopus 로고    scopus 로고
    • An identification problem in the theory of water infiltration in soils. Annals of University of Craiova
    • G. Marinoschi: An identification problem in the theory of water infiltration in soils. Annals of University of Craiova, Math. Comp. Sci. Ser., 32, 188-199 (2005)
    • (2005) Math. Comp. Sci. Ser. , vol.32 , pp. 188-199
    • Marinoschi, G.1
  • 91
    • 33645753470 scopus 로고    scopus 로고
    • Identification of the Rain Rate for a Boundary Value Problem of a Rainfall Infiltration in a Porous Medium
    • G. Marinoschi, G. Wang: Identification of the Rain Rate for a Boundary Value Problem of a Rainfall Infiltration in a Porous Medium. Numer. Funct. Anal. Optim., 27, 2, 189-205 (2006)
    • (2006) Numer. Funct. Anal. Optim. , vol.27 , Issue.2 , pp. 189-205
    • Marinoschi, G.1    Wang, G.2
  • 92
    • 33645781967 scopus 로고    scopus 로고
    • Identification of the rain rate for a boundary value problem of a rainfall infiltration in a porous medium. II Determination of the conditions of optimality
    • G. Marinoschi, G. Wang: Identification of the rain rate for a boundary value problem of a rainfall infiltration in a porous medium. II Determination of the conditions of optimality, Numer. Funct. Anal. Optim., 27, 2, 207-236 (2006)
    • (2006) Numer. Funct. Anal. Optim. , vol.27 , Issue.2 , pp. 207-236
    • Marinoschi, G.1    Wang, G.2
  • 94
    • 0142259302 scopus 로고    scopus 로고
    • Universal blow-up rates for a semilinear heat equation and applications
    • J. Matos, Ph. Souplet: Universal blow-up rates for a semilinear heat equation and applications. Adv. Differential Equations, 8, 5, 615-639 (2003)
    • (2003) Adv. Differential Equations , vol.8 , Issue.5 , pp. 615-639
    • Matos, J.1    Souplet, Ph.2
  • 96
    • 84972488065 scopus 로고
    • Monotone (nonlinear) operators in Hilbert space
    • G. Minty: Monotone (nonlinear) operators in Hilbert space. Duke Math. J., 29, 341-346 (1962)
    • (1962) Duke Math. J. , vol.29 , pp. 341-346
    • Minty, G.1
  • 98
    • 0001217997 scopus 로고
    • The Cauchy problem and boundary value problems for equations of the type of nonstationary filtration
    • O. A. Oleinik, A. S. Kalashnikov, Chzou Yui-Lin: The Cauchy problem and boundary value problems for equations of the type of nonstationary filtration. Izv. Akad. Nauk. SSSR Ser. Mat., 22, 667-704 (1958)
    • (1958) Izv. Akad. Nauk. SSSR Ser. Mat. , vol.22 , pp. 667-704
    • Oleinik, O.A.1    Kalashnikov, A.S.2    Yui-Lin, C.3
  • 99
    • 0030579044 scopus 로고    scopus 로고
    • 1-contraction and uniqueness for quasilinear elliptic-parabolic equations
    • 1-contraction and uniqueness for quasilinear elliptic-parabolic equations. J. Differential Equations, 131, 20-38 (1996)
    • (1996) J. Differential Equations , vol.131 , pp. 20-38
    • Otto, F.1
  • 100
    • 1542631305 scopus 로고    scopus 로고
    • 1-contraction and uniqueness for unstationary saturated-unsaturated porous media flow
    • 1-contraction and uniqueness for unstationary saturated-unsaturated porous media flow. Adv. Math. Sci. Appl., 7, 537-553 (1997)
    • (1997) Adv. Math. Sci. Appl. , vol.7 , pp. 537-553
    • Otto, F.1
  • 104
    • 0000543717 scopus 로고
    • The theory of infiltration
    • J. R. Philip: The theory of infiltration. Soil Sci., 7, 85, 333-337 (1958)
    • (1958) Soil Sci. , vol.7 , Issue.85 , pp. 333-337
    • Philip, J.R.1
  • 105
    • 84934731571 scopus 로고
    • On solving the unsaturated flow equation: 1. The flux-concentration relation
    • J. R. Philip: On solving the unsaturated flow equation: 1. The flux-concentration relation. Soil Sci., 116, 5, 328-336 (1973)
    • (1973) Soil Sci. , vol.116 , Issue.5 , pp. 328-336
    • Philip, J.R.1
  • 106
    • 84934740926 scopus 로고
    • On solving the unsaturated flow equation: 3. New quasi-analytical technique
    • J. R. Philip, J. H. Knight: On solving the unsaturated flow equation: 3. New quasi-analytical technique. Soil Sci., 117, 1, 1-13 (1974)
    • (1974) Soil Sci. , vol.117 , Issue.1 , pp. 1-13
    • Philip, J.R.1    Knight, J.H.2
  • 107
    • 85171297352 scopus 로고
    • Comments on steady infiltration from spherical cavities
    • J. R. Philip: Reply to "Comments on steady infiltration from spherical cavities". Soil Sci. Soc. Am. J., 49, 788-789 (1985)
    • (1985) Soil Sci. Soc. Am. J. , vol.49 , pp. 788-789
    • Philip, J.R.1    To, R.2
  • 108
    • 34247647193 scopus 로고
    • Capillary conduction of liquids through porous mediums
    • L. A. Richards: Capillary conduction of liquids through porous mediums. Physics (NY), 1, 318-333 (1931)
    • (1931) Physics (NY) , vol.1 , pp. 318-333
    • Richards, L.A.1
  • 110
    • 0002437371 scopus 로고
    • Th́eorie des Distributions ̀a Valeurs Vectorielles
    • L. Schwartz: Th́eorie des Distributions ̀a Valeurs Vectorielles. Ann. Inst. Fourier, VII, VIII, 1958
    • (1958) Ann. Inst. Fourier, VII, VIII
    • Schwartz, L.1
  • 111
    • 0038505909 scopus 로고    scopus 로고
    • Properties of the fast diffusion equation and its multidimensional exact solutions
    • in Russian)
    • E. Semenov: Properties of the fast diffusion equation and its multidimensional exact solutions. Siberian Math. J., 44, 4, 680-685 (2003) (in Russian)
    • (2003) Siberian Math. J. , vol.44 , Issue.4 , pp. 680-685
    • Semenov, E.1
  • 114
    • 0005794877 scopus 로고    scopus 로고
    • Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions
    • P. Souplet: Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions. Differential Integral Equations, 15, 2, 237-256 (2002)
    • (2002) Differential Integral Equations , vol.15 , Issue.2 , pp. 237-256
    • Souplet, P.1
  • 115
    • 0003278399 scopus 로고
    • Infinite dimensional dynamical systems in mechanics and physics
    • Springer-Verlag, New-York
    • R. Temam: Infinite Dimensional Dynamical Systems in Mechanics and Physics. Applied Mathematical Sciences Series, Springer-Verlag, New-York, 68, 1988
    • (1988) Applied Mathematical Sciences Series , vol.68
    • Temam, R.1
  • 116
    • 0041288958 scopus 로고
    • Su un problema a frontiera libera di evoluzione
    • A. Torelli: Su un problema a frontiera libera di evoluzione. Boll. Un. Mat. Ital., 11, 559-570 (1975)
    • (1975) Boll. Un. Mat. Ital. , vol.11 , pp. 559-570
    • Torelli, A.1
  • 117
    • 34250248086 scopus 로고
    • Nonstationary filtration in partially saturated porous media
    • C. J. van Duyn, J. B. McLeod: Nonstationary filtration in partially saturated porous media. Arch. Rational Mech. Anal., 78, 173-198 (1982)
    • (1982) Arch. Rational Mech. Anal. , vol.78 , pp. 173-198
    • Van Duyn, C.J.1    McLeod, J.B.2
  • 118
    • 0019057216 scopus 로고
    • A closed-form equation for predicting the hydraulic conductivity of unsaturated soils
    • M. T. van Genuchten: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J., 44, 892-898 (1980)
    • (1980) Soil Sci. Soc. Am. J. , vol.44 , pp. 892-898
    • Van Genuchten, M.T.1
  • 119
    • 0000280163 scopus 로고
    • Nonexistence of solutions for nonlinear heat equations of fastdiffusion type
    • J. L. V́azquez: Nonexistence of solutions for nonlinear heat equations of fastdiffusion type. J. Math. Pures Appl., 71, 503-526 (1992)
    • (1992) J. Math. Pures Appl. , vol.71 , pp. 503-526
    • V́azquez, J.L.1
  • 120
    • 17144451219 scopus 로고    scopus 로고
    • Darcy's law and the theory of shrinking solutions of fast diffusion equations
    • J. L. V́azquez: Darcy's law and the theory of shrinking solutions of fast diffusion equations. SIAM J. Math. Anal., 35, 4, 1005-1028 (2003)
    • (2003) SIAM J. Math. Anal. , vol.35 , Issue.4 , pp. 1005-1028
    • V́azquez, J.L.1
  • 121
    • 0041288957 scopus 로고
    • Existence results for some free boundary filtration problems
    • A. Visintin: Existence results for some free boundary filtration problems. Ann. Mat. Pura Appl., 124, 293-320 (1980)
    • (1980) Ann. Mat. Pura Appl. , vol.124 , pp. 293-320
    • Visintin, A.1
  • 126
    • 0036706487 scopus 로고    scopus 로고
    • Forward-backward parabolic equations and hysteresis
    • A. Visintin: Forward-backward parabolic equations and hysteresis. Calc. Var. Partial Differential Equations, 15, 115-132 (2002)
    • (2002) Calc. Var. Partial Differential Equations , vol.15 , pp. 115-132
    • Visintin, A.1
  • 128
    • 0033708587 scopus 로고    scopus 로고
    • Optimal control of parabolic differential equations with two point boundary state constraints
    • G. Wang: Optimal control of parabolic differential equations with two point boundary state constraints. SIAM J. Control Optim., 38, 5, 1639-1654 (2000)
    • (2000) SIAM J. Control Optim. , vol.38 , Issue.5 , pp. 1639-1654
    • Wang, G.1
  • 129
    • 0343006820 scopus 로고    scopus 로고
    • Optimal control of parabolic variational inequality involving state constraint
    • G. Wang: Optimal control of parabolic variational inequality involving state constraint. Nonlinear Analysis, 42, 789-801 (2000)
    • (2000) Nonlinear Analysis , vol.42 , pp. 789-801
    • Wang, G.1
  • 130
    • 0036401919 scopus 로고    scopus 로고
    • State-constrained optimal control governed by non-well-posed parabolic differential equations
    • G. Wang, L. Wang: State-constrained optimal control governed by non-well-posed parabolic differential equations. SIAM J. Control Optim., 40, 5, 1517-1539 (2002)
    • (2002) SIAM J. Control Optim. , vol.40 , Issue.5 , pp. 1517-1539
    • Wang, G.1    Wang, L.2
  • 131
    • 2342452583 scopus 로고    scopus 로고
    • Identification of nonlinearities in periodic parabolic equations
    • G. Wang, L. Wang: Identification of nonlinearities in periodic parabolic equations. Numer. Funct. Anal. Optim., 23, 1-2, 183-197 (2004)
    • (2004) Numer. Funct. Anal. Optim. , vol.23 , Issue.1-2 , pp. 183-197
    • Wang, G.1    Wang, L.2
  • 132
    • 0000266459 scopus 로고
    • Sorptivity and macroscopic capillary length relationships
    • A. W. Warrick, P. Broadbridge: Sorptivity and macroscopic capillary length relationships. Water Resources Research, 28, 2, 427-431 (1992)
    • (1992) Water Resources Research , vol.28 , Issue.2 , pp. 427-431
    • Warrick, A.W.1    Broadbridge, P.2
  • 133
    • 0023823588 scopus 로고
    • Constant rate rainfall infiltration: A versatile nonlinear model 1. Applications of solutions
    • I. White, P. Broadbridge: Constant Rate Rainfall Infiltration: A Versatile Nonlinear Model 1. Applications of Solutions. Water Resources Research, 24, 1, 155-162 (1988)
    • (1988) Water Resources Research , vol.24 , Issue.1 , pp. 155-162
    • White, I.1    Broadbridge, P.2
  • 134
    • 0004021335 scopus 로고
    • Fifth ed., Springer-Verlag, Berlin
    • K. Yosida: Functional Analysis. Fifth ed., Springer-Verlag, Berlin 1978
    • (1978) Functional Analysis
    • Yosida, K.1


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