메뉴 건너뛰기




Volumn 7, Issue 4, 2007, Pages 743-764

Existence for a degenerate diffusion problem with a nonlinear operator

Author keywords

Degenerate parabolic PDE; Flows in porous media; m accretive operators; Nonlinear parabolic PDE

Indexed keywords


EID: 38749121000     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-007-0348-1     Document Type: Article
Times cited : (4)

References (24)
  • 1
    • 0000836987 scopus 로고
    • Quasi-linear elliptic-parabolic differential equations
    • ALT, H. W. and LUCKHAUS, S., Quasi-linear elliptic-parabolic differential equations, Math. Z. 183 (1983), 311-341.
    • (1983) Math. Z , vol.183 , pp. 311-341
    • ALT, H.W.1    LUCKHAUS, S.2
  • 2
    • 0002293879 scopus 로고
    • The porous medium equation
    • Some Problems in Nonlinear Diffusion A. Fasano, M. Primicerio, eds, Springer, Berlin
    • ARONSON, D. G., The porous medium equation, In: Some Problems in Nonlinear Diffusion (A. Fasano, M. Primicerio, eds.), Lecture Notes in Mathematics 1224, Springer, Berlin, 1986.
    • (1986) Lecture Notes in Mathematics , vol.1224
    • ARONSON, D.G.1
  • 4
    • 0142023986 scopus 로고    scopus 로고
    • Existence for a time dependent rainfall infiltration model with a blowing up diffusivity, Nonlinear Analysis
    • BARBU, V. and MARINOSCHI, G., Existence for a time dependent rainfall infiltration model with a blowing up diffusivity, Nonlinear Analysis: Series B Real World Applications 5(2) (2004), 231-245.
    • (2004) Series B Real World Applications , vol.5 , Issue.2 , pp. 231-245
    • BARBU, V.1    MARINOSCHI, G.2
  • 6
    • 21844491188 scopus 로고
    • Quasilinear first-order equations with continuous nonlinearities
    • BÉNILAN, P. and KRUSHKOV, S. N., Quasilinear first-order equations with continuous nonlinearities, Russian Acad. Sci. Dokl. Math. 50(3) (1995), 391-396.
    • (1995) Russian Acad. Sci. Dokl. Math , vol.50 , Issue.3 , pp. 391-396
    • BÉNILAN, P.1    KRUSHKOV, S.N.2
  • 7
    • 4344603515 scopus 로고    scopus 로고
    • On the infiltration of rain water through the soil with runoff of the excess water
    • BORSI, I. and FARINA, A. and FASANO, A., On the infiltration of rain water through the soil with runoff of the excess water, Nonlinear Analysis Real World Applications 5 (2004), 763-800.
    • (2004) Nonlinear Analysis Real World Applications , vol.5 , pp. 763-800
    • BORSI, I.1    FARINA, A.2    FASANO, A.3
  • 9
    • 0033407951 scopus 로고    scopus 로고
    • Entropy solutions for nonlinear degenerate problems
    • CARILLO, J., Entropy solutions for nonlinear degenerate problems, Arch. Rational Mech. Anal. 147 (1999), 269-361.
    • (1999) Arch. Rational Mech. Anal , vol.147 , pp. 269-361
    • CARILLO, J.1
  • 10
    • 0033587465 scopus 로고    scopus 로고
    • Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems
    • CARILLO, J. and WITTBOLD, P., Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems, J. Differential Equations 156 (1999), 93-121.
    • (1999) J. Differential Equations , vol.156 , pp. 93-121
    • CARILLO, J.1    WITTBOLD, P.2
  • 11
    • 0036026066 scopus 로고    scopus 로고
    • Theory of extended solutions for fast diffusion equations in optimal classes of data. Radiation from singularities
    • CHASSEIGNE, E. and VÁZQUEZ, J. L., Theory of extended solutions for fast diffusion equations in optimal classes of data. Radiation from singularities, Archive Rat. Mech. Anal. 164 (2002), 133-187.
    • (2002) Archive Rat. Mech. Anal , vol.164 , pp. 133-187
    • CHASSEIGNE, E.1    VÁZQUEZ, J.L.2
  • 12
    • 1142271128 scopus 로고    scopus 로고
    • Approximation results for semigroups generated by multivalued linear-operators and applications
    • FAVINI, A. and FUHRMAN, M., Approximation results for semigroups generated by multivalued linear-operators and applications, Differential and Integral Equations 11(5) (1998), 781-805.
    • (1998) Differential and Integral Equations , vol.11 , Issue.5 , pp. 781-805
    • FAVINI, A.1    FUHRMAN, M.2
  • 14
    • 4444318875 scopus 로고    scopus 로고
    • Quasilinear degenerate evolution equations in Banach spaces
    • FAVINI, A. and YAGI, A., Quasilinear degenerate evolution equations in Banach spaces, J. Evol. Eq. 4 (2004), 421-449.
    • (2004) J. Evol. Eq , vol.4 , pp. 421-449
    • FAVINI, A.1    YAGI, A.2
  • 17
    • 0000604204 scopus 로고
    • Generalized solutions of the Cauchy problem in the large for first-order nonlinear equations
    • KRUSHKOV, S. N., Generalized solutions of the Cauchy problem in the large for first-order nonlinear equations, Soviet Math.. Dokl. 10 (1969), 785-788.
    • (1969) Soviet Math.. Dokl , vol.10 , pp. 785-788
    • KRUSHKOV, S.N.1
  • 18
    • 0142078131 scopus 로고    scopus 로고
    • Nonlinear infiltration with a singular diffusion coefficient
    • MARINOSCHI, G., Nonlinear infiltration with a singular diffusion coefficient, Differential Integral Equations 16(9) (2003), 1093-1110.
    • (2003) Differential Integral Equations , vol.16 , Issue.9 , pp. 1093-1110
    • MARINOSCHI, G.1
  • 19
    • 10844239004 scopus 로고    scopus 로고
    • A free boundary problem describing the saturated unsaturated flow in a porous medium
    • MARINOSCHI, G., A free boundary problem describing the saturated unsaturated flow in a porous medium, Abstract and Applied Analysis 2004(9) (2004), 729-755.
    • (2004) Abstract and Applied Analysis , vol.2004 , Issue.9 , pp. 729-755
    • MARINOSCHI, G.1
  • 21
    • 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 (1997), 537-553.
    • (1997) Adv. Math. Sci. Appl , vol.7 , pp. 537-553
    • OTTO, F.1
  • 22
    • 17144451219 scopus 로고    scopus 로고
    • Darcy's law and the theory of shrinking solutions of fast diffusion equations
    • VÁZQUEZ, J. L., Darcy's law and the theory of shrinking solutions of fast diffusion equations, SIAM J. Math. Anal. 35(A) (2003), 1005-1028.
    • (2003) SIAM J. Math. Anal , vol.35 , Issue.A , pp. 1005-1028
    • VÁZQUEZ, J.L.1
  • 23
    • 16344394053 scopus 로고    scopus 로고
    • Symmetrization and mass comparison for degenerate nonlinear parabolic and related elliptic equations
    • VÁZQUEZ, J. L., Symmetrization and mass comparison for degenerate nonlinear parabolic and related elliptic equations, Advanced Nonlinear Studies 5 (2005), 87-131.
    • (2005) Advanced Nonlinear Studies , vol.5 , pp. 87-131
    • VÁZQUEZ, J.L.1
  • 24
    • 34547843765 scopus 로고    scopus 로고
    • Smoothing and Decay Estimates for Nonlinear Diffusion Equations. Equations of Porous Medium Type
    • Oxford University Press
    • VÁZQUEZ, J. L., Smoothing and Decay Estimates for Nonlinear Diffusion Equations. Equations of Porous Medium Type, Series Oxford Lecture Series in Mathematics and its Applications 33, Oxford University Press, 2006.
    • (2006) Series Oxford Lecture Series in Mathematics and its Applications , vol.33
    • VÁZQUEZ, J.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.