메뉴 건너뛰기




Volumn 320, Issue 1, 2001, Pages 87-113

Linear and nonlinear heat equations in Lδq spaces and universal bounds for global solutions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035592132     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004471     Document Type: Article
Times cited : (58)

References (37)
  • 1
    • 0004050913 scopus 로고    scopus 로고
    • Global existence and finite-time blowup for a class of nonlocal parabolic problems
    • J. W. Bebernes, A. A. Lacey, Global existence and finite-time blowup for a class of nonlocal parabolic problems, Adv. Diff. Equations 2 (1997), 927-953
    • (1997) Adv. Diff. Equations , vol.2 , pp. 927-953
    • Bebernes, J.W.1    Lacey, A.A.2
  • 2
    • 21844518574 scopus 로고
    • Remarks on the preceding paper by M. Ben-Artzi "Global solutions of two-dimensional Navier-Stokes and Euler equations"
    • H. Brézis, Remarks on the preceding paper by M. Ben-Artzi "Global solutions of two-dimensional Navier-Stokes and Euler equations", Arch. Rational Mech. Anal. 128 (1994) 359-360
    • (1994) Arch. Rational Mech. Anal. , vol.128 , pp. 359-360
    • Brézis, H.1
  • 3
    • 0347565270 scopus 로고    scopus 로고
    • Some simple nonlinear PDE's without solutions
    • H. Brézis, X. Cabré, Some simple nonlinear PDE's without solutions, Bull. Un. Mat. Ital. 1 (1998), 223-262
    • (1998) Bull. Un. Mat. Ital. , vol.1 , pp. 223-262
    • Brézis, H.1    Cabré, X.2
  • 4
    • 0030443821 scopus 로고    scopus 로고
    • A nonlinear heat equation with singular initial data
    • H. Brézis, T. Cazenave, A nonlinear heat equation with singular initial data, J. Analyse Math. 68 (1996), 877-894
    • (1996) J. Analyse Math. , vol.68 , pp. 877-894
    • Brézis, H.1    Cazenave, T.2
  • 6
    • 0002553191 scopus 로고    scopus 로고
    • Weak eigenfunctions for the linearization of extremal elliptic problems
    • X. Cabré, Y. Martel, Weak eigenfunctions for the linearization of extremal elliptic problems, J. Funct. Anal. 156 (1998), 30-56
    • (1998) J. Funct. Anal. , vol.156 , pp. 30-56
    • Cabré, X.1    Martel, Y.2
  • 7
    • 0033472884 scopus 로고    scopus 로고
    • Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier
    • Série I
    • X. Cabré, Y Martel, Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier, C. R. Acad. Sc. Paris, Série I, 329 (1999), 973-978
    • (1999) C. R. Acad. Sc. Paris , vol.329 , pp. 973-978
    • Cabré, X.1    Martel, Y.2
  • 8
    • 84950012263 scopus 로고
    • Solutions globales d'équations de la chaleur semilinéaires
    • T. Cazenave, P. L. Lions, Solutions globales d'équations de la chaleur semilinéaires, Commun. Partial Differ. Equations 9 (1984), 955-978
    • (1984) Commun. Partial Differ. Equations , vol.9 , pp. 955-978
    • Cazenave, T.1    Lions, P.L.2
  • 9
    • 0002634193 scopus 로고
    • Stationary solutions, blow-up and convergence to stationary solutions for semi-linear parabolic equations with nonlinear boundary conditions
    • M. Chipot, M. Fila, P. Quittner, Stationary solutions, blow-up and convergence to stationary solutions for semi-linear parabolic equations with nonlinear boundary conditions, Acta Math. Univ. Comenianae 60 (1991), 35-103
    • (1991) Acta Math. Univ. Comenianae , vol.60 , pp. 35-103
    • Chipot, M.1    Fila, M.2    Quittner, P.3
  • 10
    • 0000788993 scopus 로고
    • Boundedness of global solutions for the heat equation with nonlinear boundary conditions
    • M. Fila, Boundedness of global solutions for the heat equation with nonlinear boundary conditions, Comm. Math. Univ. Carol. 30 (1989), 479-484
    • (1989) Comm. Math. Univ. Carol. , vol.30 , pp. 479-484
    • Fila, M.1
  • 11
    • 38249009228 scopus 로고
    • Boundedness of global solutions of nonlinear diffusion equations
    • M. Fila, Boundedness of global solutions of nonlinear diffusion equations, J. Differ. Equations 98 (1992), 226-240
    • (1992) J. Differ. Equations , vol.98 , pp. 226-240
    • Fila, M.1
  • 12
    • 0039419119 scopus 로고    scopus 로고
    • Boundedness of global solutions of nonlocal parabolic equations
    • M. Fila, Boundedness of global solutions of nonlocal parabolic equations, Nonlin. Anal. TMA 30 (1997), 877-885
    • (1997) Nonlin. Anal. TMA , vol.30 , pp. 877-885
    • Fila, M.1
  • 13
    • 0031341329 scopus 로고    scopus 로고
    • On the boundedness of global solutions of abstract semi-linear parabolic equations
    • M. Fila, H. A. Levine, On the boundedness of global solutions of abstract semi-linear parabolic equations, J. Math. Anal. Appl. 216 (1997), 654-666
    • (1997) J. Math. Anal. Appl. , vol.216 , pp. 654-666
    • Fila, M.1    Levine, H.A.2
  • 14
    • 0042237449 scopus 로고    scopus 로고
    • Global solutions of a semilinear parabolic equation
    • M. Fila, P. Poláčik, Global solutions of a semilinear parabolic equation, Adv. Diff. Equations 4 (1999), 163-196
    • (1999) Adv. Diff. Equations , vol.4 , pp. 163-196
    • Fila, M.1    Poláčik, P.2
  • 15
    • 0031257438 scopus 로고    scopus 로고
    • Global solutions of the Laplace equation with a nonlinear dynamical boundary condition
    • M. Fila, P. Quittner, Global solutions of the Laplace equation with a nonlinear dynamical boundary condition, Math. Methods Appl. Sci. 20 (1997), 1325-1333
    • (1997) Math. Methods Appl. Sci. , vol.20 , pp. 1325-1333
    • Fila, M.1    Quittner, P.2
  • 16
    • 3042714860 scopus 로고    scopus 로고
    • Large time behavior of solutions of a semilinear parabolic equation with a nonlinear dynamical boundary condition
    • Birkhäuser Verlag
    • M. Fila, P. Quittner, Large time behavior of solutions of a semilinear parabolic equation with a nonlinear dynamical boundary condition, in: Topics in Nonlinear Analysis, The Herbert Amann Anniversary Volume, Birkhäuser Verlag, 1998, 251-272
    • (1998) Topics in Nonlinear Analysis, the Herbert Amann Anniversary Volume , pp. 251-272
    • Fila, M.1    Quittner, P.2
  • 17
    • 0031541195 scopus 로고    scopus 로고
    • Continuation of blow-up solutions of nonlinear heat equations in several space dimensions
    • V A. Galaktionov, J. L. Vázquez, Continuation of blow-up solutions of nonlinear heat equations in several space dimensions, Comm. Pure Appl. Math. 50 (1997), 1-67
    • (1997) Comm. Pure Appl. Math. , vol.50 , pp. 1-67
    • Galaktionov, V.A.1    Vázquez, J.L.2
  • 18
    • 0001464964 scopus 로고
    • A bound for global solutions of semi-linear heat equations
    • Y. Giga, A bound for global solutions of semi-linear heat equations, Comm. Math. Phys. 103 (1986), 415-421
    • (1986) Comm. Math. Phys. , vol.103 , pp. 415-421
    • Giga, Y.1
  • 19
    • 84980080195 scopus 로고
    • On the growth of solutions of quasilinear parabolic equations
    • S. Kaplan, On the growth of solutions of quasilinear parabolic equations, Comm. Pure Appl. Math. 16 (1963), 327-330
    • (1963) Comm. Pure Appl. Math. , vol.16 , pp. 327-330
    • Kaplan, S.1
  • 20
    • 0000911759 scopus 로고
    • m, with applications to weak solutions
    • m, with applications to weak solutions, Math. Z. 187 (1984), 471-480
    • (1984) Math. Z. , vol.187 , pp. 471-480
    • Kato, T.1
  • 21
    • 84948486085 scopus 로고
    • Remarks on the large time behaviour of a nonlinear diffusion equation
    • O. Kavian, Remarks on the large time behaviour of a nonlinear diffusion equation, Ann. Inst. H. Poincaré, Anal. Non-linéaire 4 (1987), 423-452
    • (1987) Ann. Inst. H. Poincaré, Anal. Non-linéaire , vol.4 , pp. 423-452
    • Kavian, O.1
  • 22
    • 84988164328 scopus 로고
    • Study of global solutions of parabolic equations via apriori estimates. Part I: Equations with principal elliptic part equal to the Laplacian
    • G. M. Lieberman, Study of global solutions of parabolic equations via apriori estimates. Part I: equations with principal elliptic part equal to the Laplacian, Math. Methods Appl. Sci. 16 (1993), 457-474
    • (1993) Math. Methods Appl. Sci. , vol.16 , pp. 457-474
    • Lieberman, G.M.1
  • 23
    • 0011049912 scopus 로고
    • Study of global solutions of parabolic equations via a priori estimates. Part II: Porous medium equations
    • G. M. Lieberman, Study of global solutions of parabolic equations via a priori estimates. Part II: porous medium equations, Comm. Appl. Nonlin. Anal. 1 (1994), 93-114
    • (1994) Comm. Appl. Nonlin. Anal. , vol.1 , pp. 93-114
    • Lieberman, G.M.1
  • 24
    • 0043118979 scopus 로고    scopus 로고
    • Study of global solutions of parabolic equations via apriori estimates. Part III: Equations of p-Laplacian type
    • Banach Center Publications, PWN, Warszawa
    • G. M. Lieberman, Study of global solutions of parabolic equations via apriori estimates. Part III: Equations of p-Laplacian type, in: Singularities and Differential Equations, Banach Center Publications, Vol. 33, PWN, Warszawa, 1996, 199-221
    • (1996) Singularities and Differential Equations , vol.33 , pp. 199-221
    • Lieberman, G.M.1
  • 26
    • 0032159629 scopus 로고    scopus 로고
    • Estimations optimales en temps petit et près de la frontière pour les solutions de l'équation de la chaleur avec données non-compatibles
    • Série I
    • Y. Martel, Ph. Souplet, Estimations optimales en temps petit et près de la frontière pour les solutions de l'équation de la chaleur avec données non-compatibles, C. R. Acad. Sc. Paris, Série I, 327 (1998), 575-580
    • (1998) C. R. Acad. Sc. Paris , vol.327 , pp. 575-580
    • Martel, Y.1    Souplet, Ph.2
  • 27
    • 0034195698 scopus 로고    scopus 로고
    • Small time boundary behavior of solutions of parabolic equations with noncompatible data
    • Y. Martel, Ph. Souplet, Small time boundary behavior of solutions of parabolic equations with noncompatible data, J. Math. Pures et Appliquées 79 (2000), 603-632
    • (2000) J. Math. Pures et Appliquées , vol.79 , pp. 603-632
    • Martel, Y.1    Souplet, Ph.2
  • 28
    • 0002842122 scopus 로고
    • On the asymptotic behavior of solutions of certain quasi-linear equations of parabolic type
    • W. M. Ni, P. E. Sacks, J. Tavantzis, On the asymptotic behavior of solutions of certain quasi-linear equations of parabolic type, J. Differ. Equations 54 (1984), 97-120
    • (1984) J. Differ. Equations , vol.54 , pp. 97-120
    • Ni, W.M.1    Sacks, P.E.2    Tavantzis, J.3
  • 29
    • 0037887545 scopus 로고    scopus 로고
    • A priori bounds for global solutions of a semilinear parabolic problem
    • P. Quittner, A priori bounds for global solutions of a semilinear parabolic problem, Acta Math. Univ. Comenianae 68 (1999), 195-203
    • (1999) Acta Math. Univ. Comenianae , vol.68 , pp. 195-203
    • Quittner, P.1
  • 31
    • 0011045192 scopus 로고    scopus 로고
    • Sur l'asymptotique des solutions globales pour une équation de la chaleur semi-linéaire dans des domaines non bornés
    • Série I
    • Ph. Souplet, Sur l'asymptotique des solutions globales pour une équation de la chaleur semi-linéaire dans des domaines non bornés, C. R. Acad. Sci. Paris, Série I, 323 (1996), 877-882
    • (1996) C. R. Acad. Sci. Paris , vol.323 , pp. 877-882
    • Souplet, Ph.1
  • 32
    • 0033474488 scopus 로고    scopus 로고
    • Geometry of unbounded domains, Poincaré inequalities, and stability in semilinear parabolic equations
    • Ph. Souplet, Geometry of unbounded domains, Poincaré inequalities, and stability in semilinear parabolic equations, Commun. Partial Differ. Equations 24 (1999), 951-973
    • (1999) Commun. Partial Differ. Equations , vol.24 , pp. 951-973
    • Souplet, Ph.1
  • 33
    • 0040682296 scopus 로고    scopus 로고
    • Boundedness of global solutions of one dimensional quasi-linear parabolic equations
    • R. Suzuki, Boundedness of global solutions of one dimensional quasi-linear parabolic equations, J. Math. Soc. Japan 50 (1998), 119-138
    • (1998) J. Math. Soc. Japan , vol.50 , pp. 119-138
    • Suzuki, R.1
  • 34
    • 0001404928 scopus 로고
    • Semilinear evolution equations in Banach spaces
    • F. B. Weissler, Semilinear evolution equations in Banach spaces, J. Functional Analysis 32 (1979), 277-296
    • (1979) J. Functional Analysis , vol.32 , pp. 277-296
    • Weissler, F.B.1
  • 36
    • 51249183619 scopus 로고
    • Existence and nonexistence of global solutions for a semilinear heat equation
    • F. B. Weissler, Existence and nonexistence of global solutions for a semilinear heat equation, Israel J. Math. 38 (1981), 29-40
    • (1981) Israel J. Math. , vol.38 , pp. 29-40
    • Weissler, F.B.1
  • 37
    • 0000416165 scopus 로고
    • p-energy and blow-up for a semilinear heat equation
    • p-energy and blow-up for a semilinear heat equation, Proc. Symp. Pure Math. 45 (1986), 545-551
    • (1986) Proc. Symp. Pure Math. , vol.45 , pp. 545-551
    • Weissler, F.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.