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Volumn 225, Issue 1, 2005, Pages 33-62

Asymptotics of the porous media equation via Sobolev inequalities

Author keywords

Asymptotics; Logarithmic Sobler inequalities; Porous media equation

Indexed keywords


EID: 21044445926     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2005.03.011     Document Type: Article
Times cited : (44)

References (36)
  • 1
    • 0000828237 scopus 로고
    • Large time behaviour of solutions of Neumann boundary value problem for the porous medium equation
    • N.D. Alikakos R. Rostamian Large time behaviour of solutions of Neumann boundary value problem for the porous medium equation Indiana Univ. J. Math. 30 1981 749-785
    • (1981) Indiana Univ. J. Math. , vol.30 , pp. 749-785
    • Alikakos, N.D.1    Rostamian, R.2
  • 2
    • 21044442958 scopus 로고
    • Regularity of flows in porous medium: A survey
    • 1986 Nonlinear Diffusion Equations and Their Equilibrium States, Berkeley, CA
    • D.G. Aronson, Regularity of flows in porous medium: A survey, in: Nonlinear Diffusion Equations and Their Equilibrium States, Berkeley, CA, 1986, Math. Sci. Res. Inst. Publ. 12 (1988).
    • (1988) Math. Sci. Res. Inst. Publ. , vol.12
    • Aronson, D.G.1
  • 4
    • 0001510540 scopus 로고
    • Large time behaviour of solutions of the porous medium equation in bounded domains
    • D.G. Aronson L.A. Peletier Large time behaviour of solutions of the porous medium equation in bounded domains J. Differential Equations 39 1981 378-412
    • (1981) J. Differential Equations , vol.39 , pp. 378-412
    • Aronson, D.G.1    Peletier, L.A.2
  • 9
    • 84974004482 scopus 로고
    • Optimal smoothing and decay estimates for viscuously damped conservation lows, with applications to the 2-D Navier Stokes equation
    • E. Carlen M. Loss Optimal smoothing and decay estimates for viscuously damped conservation lows, with applications to the 2-D Navier Stokes equation Duke Math. J. 81 1995 135-157
    • (1995) Duke Math. J. , vol.81 , pp. 135-157
    • Carlen, E.1    Loss, M.2
  • 10
    • 0003277699 scopus 로고    scopus 로고
    • 1-decay of solutions of the porous medium equation to self-similarity
    • 1-decay of solutions of the porous medium equation to self-similarity Indiana Univ. J. Math. 49 2000 113-142
    • (2000) Indiana Univ. J. Math. , vol.49 , pp. 113-142
    • Carrillo, J.A.1    Toscani, G.2
  • 11
    • 0031534574 scopus 로고    scopus 로고
    • Inégalités de Faber-Krahn et inclusion de Sobolev-Orlicz
    • G. Carron Inégalités de Faber-Krahn et inclusion de Sobolev-Orlicz Potential Anal. 7 1997 555-575
    • (1997) Potential Anal. , vol.7 , pp. 555-575
    • Carron, G.1
  • 12
    • 0035923495 scopus 로고    scopus 로고
    • Uniform bounds for solutions to quasilinear parabolic equations
    • F. Cipriani G. Grillo Uniform bounds for solutions to quasilinear parabolic equations J. Differential Equations 177 2001 209-234
    • (2001) J. Differential Equations , vol.177 , pp. 209-234
    • Cipriani, F.1    Grillo, G.2
  • 13
    • 0036600918 scopus 로고    scopus 로고
    • ∞ Hölder continuity for quasilinear parabolic equations associated to Sobolev derivations
    • ∞ Hölder continuity for quasilinear parabolic equations associated to Sobolev derivations J. Math. Anal. Appl. 270 2002 267-290
    • (2002) J. Math. Anal. Appl. , vol.270 , pp. 267-290
    • Cipriani, F.1    Grillo, G.2
  • 14
    • 0141815518 scopus 로고    scopus 로고
    • Nonlinear markovian semigroups and nonlinear Dirichlet forms
    • F. Cipriani G. Grillo Nonlinear markovian semigroups and nonlinear Dirichlet forms J. Reine Angew. Math. 562 2003 201-235
    • (2003) J. Reine Angew. Math. , vol.562 , pp. 201-235
    • Cipriani, F.1    Grillo, G.2
  • 16
    • 0000573290 scopus 로고
    • Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
    • E.B. Davies B. Simon Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians J. Functional Anal. 59 1984 335-395
    • (1984) J. Functional Anal. , vol.59 , pp. 335-395
    • Davies, E.B.1    Simon, B.2
  • 17
    • 0012740123 scopus 로고    scopus 로고
    • Generalized Sobolev inequalities and asymptotic behaviour in fast diffusion and porous medium problem
    • Preprint Ceremade 9905 available at
    • M. del Pino, J. Dolbeault, Generalized Sobolev inequalities and asymptotic behaviour in fast diffusion and porous medium problem, Preprint Ceremade 9905, 1999, available at http://www.ceremade.dauphine.fr/~dolbeaul/Preprints/GLSFD6.ps.
    • (1999)
    • del Pino, M.1    Dolbeault, J.2
  • 18
    • 0036710614 scopus 로고    scopus 로고
    • Best constant for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions
    • M. del Pino J. Dolbeault Best constant for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions J. Math. Pures Appl. 81 2002 847-875
    • (2002) J. Math. Pures Appl. , vol.81 , pp. 847-875
    • del Pino, M.1    Dolbeault, J.2
  • 19
    • 84961469235 scopus 로고
    • Hölder estimates for nonlinear degenerate parabolic systems
    • E. DiBenedetto A. Friedman Hölder estimates for nonlinear degenerate parabolic systems J. Reine Angew. Math. 357 1985 1-22
    • (1985) J. Reine Angew. Math. , vol.357 , pp. 1-22
    • DiBenedetto, E.1    Friedman, A.2
  • 20
    • 0013163910 scopus 로고
    • Applications of nonlinear semigroup theory to certain partial differential equations
    • Academic Press New York
    • L.C. Evans Applications of nonlinear semigroup theory to certain partial differential equations M.G. Crandall Nonlinear Evolution Equations 1978 Academic Press New York 163-188
    • (1978) Nonlinear Evolution Equations , pp. 163-188
    • Evans, L.C.1
  • 21
    • 84968502599 scopus 로고
    • The asymptotic behaviour of gas in an n-dimensional porous medium
    • A. Friedman S. Kamin The asymptotic behaviour of gas in an n-dimensional porous medium Trans. AMS 262 1980 551-563
    • (1980) Trans. AMS , vol.262 , pp. 551-563
    • Friedman, A.1    Kamin, S.2
  • 22
    • 0001429116 scopus 로고
    • Logarithmic Sobolev inequalities
    • L. Gross Logarithmic Sobolev inequalities Amer. J. Math. 97 1976 1061-1083
    • (1976) Amer. J. Math. , vol.97 , pp. 1061-1083
    • Gross, L.1
  • 23
    • 0003228562 scopus 로고    scopus 로고
    • Sobolev spaces on Riemannian manifolds
    • Springer Berlin
    • E. Hebey Sobolev spaces on Riemannian manifolds Lecture Notes in Mathematics vol. 1635 1996 Springer Berlin
    • (1996) Lecture Notes in Mathematics , vol.1635
    • Hebey, E.1
  • 24
    • 0013167197 scopus 로고    scopus 로고
    • Large time behaviour of the solutions to some degenerate parabolic equations
    • N. Igbida Large time behaviour of the solutions to some degenerate parabolic equations Comm. Partial Differential Equations 26 2001 1385-1408
    • (2001) Comm. Partial Differential Equations , vol.26 , pp. 1385-1408
    • Igbida, N.1
  • 25
    • 0002701304 scopus 로고
    • Asymptotic behaviour of solutions of the porous medium equation with changing sign
    • S. Kamin J.L. Vázquez Asymptotic behaviour of solutions of the porous medium equation with changing sign SIAM J. Math. Anal. 22 1991 34-45
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 34-45
    • Kamin, S.1    Vázquez, J.L.2
  • 26
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: The porous medium equation
    • F. Otto The geometry of dissipative evolution equations: The porous medium equation Comm. Partial Differential Equations 26 2001 101-174
    • (2001) Comm. Partial Differential Equations , vol.26 , pp. 101-174
    • Otto, F.1
  • 27
    • 51249183526 scopus 로고
    • The Lyapunov method for semigroups of nonlinear contractions in Banach spaces
    • A. Pazy The Lyapunov method for semigroups of nonlinear contractions in Banach spaces J. Analyse Math. 40 1981 239-262
    • (1981) J. Analyse Math. , vol.40 , pp. 239-262
    • Pazy, A.1
  • 29
    • 0041383085 scopus 로고    scopus 로고
    • Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations
    • AMS Providence, RI
    • R.E. Showalter Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations AMS Mathematical Surveys and Monographs vol. 49 1996 AMS Providence, RI
    • (1996) AMS Mathematical Surveys and Monographs , vol.49
    • Showalter, R.E.1
  • 31
    • 0000383614 scopus 로고
    • An introduction to the mathematical theory of the porous medium equation
    • Shape Optimization and Free Boundaries
    • J.L. Vázquez, An introduction to the mathematical theory of the porous medium equation, in: Shape Optimization and Free Boundaries, NATO ASI Ser., Ser. C, vol. 380, 1992, pp. 347-389.
    • (1992) NATO ASI Ser. Ser. C , vol.380 , pp. 347-389
    • Vázquez, J.L.1
  • 32
    • 0000383614 scopus 로고
    • An introduction to the mathematical theory of the porous medium equation
    • J.L. Vázquez An introduction to the mathematical theory of the porous medium equation Adv. Sci. Ser. C. Math. Phys. Sci. 380 1992 347-389
    • (1992) Adv. Sci. Ser. C. Math. Phys. Sci. , vol.380 , pp. 347-389
    • Vázquez, J.L.1
  • 33
    • 0009191281 scopus 로고    scopus 로고
    • Asymptotic behaviour for the porous medium equation in the whole space
    • Notas del curso de doctorado
    • J.L. Vázquez, Asymptotic behaviour for the porous medium equation in the whole space, Notas del curso de doctorado, 1997.
    • (1997)
    • Vázquez, J.L.1
  • 34
    • 0009191281 scopus 로고    scopus 로고
    • Asymptotic behaviour for the porous medium equation in a bounded domain
    • The Dirichlet problem, Notas del Curso de Doctorado
    • J.L. Vázquez, Asymptotic behaviour for the porous medium equation in a bounded domain, The Dirichlet problem, Notas del Curso de Doctorado, 1997.
    • (1997)
    • Vázquez, J.L.1
  • 35
    • 0037847744 scopus 로고    scopus 로고
    • Asymptotic behaviour for the porous medium equation in the whole space
    • J.L. Vázquez Asymptotic behaviour for the porous medium equation in the whole space J. Evol. Equ. 3 2003 67-118
    • (2003) J. Evol. Equ. , vol.3 , pp. 67-118
    • Vázquez, J.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.