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Volumn 246, Issue 10, 2009, Pages 3902-3931

On convergence of solutions to equilibria for quasilinear parabolic problems

Author keywords

Center manifolds; Free boundary problems; Nonlinear boundary conditions; Normally stable; Quasilinear parabolic equations; Travelling waves

Indexed keywords


EID: 63449140742     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2008.10.034     Document Type: Article
Times cited : (85)

References (29)
  • 1
    • 84972541997 scopus 로고
    • Dynamic theory of quasilinear parabolic equations. II. Reaction-diffusion systems
    • Amann H. Dynamic theory of quasilinear parabolic equations. II. Reaction-diffusion systems. Differential Integral Equations 3 (1990) 13-75
    • (1990) Differential Integral Equations , vol.3 , pp. 13-75
    • Amann, H.1
  • 2
    • 0007388536 scopus 로고
    • Linear and Quasilinear Parabolic Problems, vol. I. Abstract Linear Theory
    • Birkhäuser, Boston, MA
    • Amann H. Linear and Quasilinear Parabolic Problems, vol. I. Abstract Linear Theory. Monogr. Math. vol. 89 (1995), Birkhäuser, Boston, MA
    • (1995) Monogr. Math. , vol.89
    • Amann, H.1
  • 3
    • 10944244690 scopus 로고    scopus 로고
    • Maximal regularity for nonautonomous evolution equations
    • Amann H. Maximal regularity for nonautonomous evolution equations. Adv. Nonlinear Stud. 4 (2004) 417-430
    • (2004) Adv. Nonlinear Stud. , vol.4 , pp. 417-430
    • Amann, H.1
  • 4
    • 33646405408 scopus 로고    scopus 로고
    • Quasilinear parabolic problems via maximal regularity
    • Amann H. Quasilinear parabolic problems via maximal regularity. Adv. Differential Equations 10 (2005) 1081-1110
    • (2005) Adv. Differential Equations , vol.10 , pp. 1081-1110
    • Amann, H.1
  • 5
    • 0003226107 scopus 로고
    • Continuous and Discrete Dynamics Near Manifolds of Equilibria
    • Springer, Berlin
    • Aulbach B. Continuous and Discrete Dynamics Near Manifolds of Equilibria. Lecture Notes in Math. vol. 1058 (1984), Springer, Berlin
    • (1984) Lecture Notes in Math. , vol.1058
    • Aulbach, B.1
  • 6
    • 0002538743 scopus 로고
    • Invariant manifolds for semilinear partial differential equations
    • Wiley, Chichester
    • Bates P., and Jones C. Invariant manifolds for semilinear partial differential equations. Dynamics Reported vol. 2 (1989), Wiley, Chichester 1-38
    • (1989) Dynamics Reported , vol.2 , pp. 1-38
    • Bates, P.1    Jones, C.2
  • 8
    • 0002600360 scopus 로고
    • Abstract parabolic quasilinear equations and applications to a groundwater flow problem
    • Clément Ph., and Li S. Abstract parabolic quasilinear equations and applications to a groundwater flow problem. Adv. Math. Sci. Appl. 3 (1994) 17-32
    • (1994) Adv. Math. Sci. Appl. , vol.3 , pp. 17-32
    • Clément, Ph.1    Li, S.2
  • 10
    • 0000964906 scopus 로고
    • Stability, instability and center manifold theorem for fully nonlinear autonomous parabolic equations in Banach space
    • Da Prato G., and Lunardi A. Stability, instability and center manifold theorem for fully nonlinear autonomous parabolic equations in Banach space. Arch. Ration. Mech. Anal. 101 (1988) 115-141
    • (1988) Arch. Ration. Mech. Anal. , vol.101 , pp. 115-141
    • Da Prato, G.1    Lunardi, A.2
  • 11
    • 0242287337 scopus 로고    scopus 로고
    • R-boundedness and problems of elliptic and parabolic type
    • Denk R., Hieber M., and Prüss J. R-boundedness and problems of elliptic and parabolic type. Mem. Amer. Math. Soc. 166 788 (2003)
    • (2003) Mem. Amer. Math. Soc. , vol.166 , Issue.788
    • Denk, R.1    Hieber, M.2    Prüss, J.3
  • 12
    • 34250882162 scopus 로고    scopus 로고
    • q-regularity for parabolic problems with inhomogeneous boundary data
    • q-regularity for parabolic problems with inhomogeneous boundary data. Math. Z. 257 (2007) 193-224
    • (2007) Math. Z. , vol.257 , pp. 193-224
    • Denk, R.1    Hieber, M.2    Prüss, J.3
  • 13
    • 54949146059 scopus 로고    scopus 로고
    • p-regularity of parabolic problems with boundary dynamics of relaxation type
    • p-regularity of parabolic problems with boundary dynamics of relaxation type. J. Funct. Anal. 255 (2008) 3149-3187
    • (2008) J. Funct. Anal. , vol.255 , pp. 3149-3187
    • Denk, R.1    Prüss, J.2    Zacher, R.3
  • 14
    • 0242338686 scopus 로고    scopus 로고
    • Analytic solutions for a Stefan problem with Gibbs-Thomson correction
    • Escher J., Prüss J., and Simonett G. Analytic solutions for a Stefan problem with Gibbs-Thomson correction. J. Reine Angew. Math. 563 (2003) 1-52
    • (2003) J. Reine Angew. Math. , vol.563 , pp. 1-52
    • Escher, J.1    Prüss, J.2    Simonett, G.3
  • 15
    • 0001025274 scopus 로고    scopus 로고
    • A center manifold analysis for the Mullins-Sekerka model
    • Escher J., and Simonett G. A center manifold analysis for the Mullins-Sekerka model. J. Differential Equations 143 (1998) 267-292
    • (1998) J. Differential Equations , vol.143 , pp. 267-292
    • Escher, J.1    Simonett, G.2
  • 16
    • 0037059123 scopus 로고    scopus 로고
    • Quasi-static motion of a capillary drop. II. The three-dimensional case
    • Friedman A., and Reitich F. Quasi-static motion of a capillary drop. II. The three-dimensional case. J. Differential Equations 186 (2002) 509-557
    • (2002) J. Differential Equations , vol.186 , pp. 509-557
    • Friedman, A.1    Reitich, F.2
  • 17
    • 21744445483 scopus 로고    scopus 로고
    • Existence results for the quasistationary motion of a free capillary liquid drop
    • Günther M., and Prokert G. Existence results for the quasistationary motion of a free capillary liquid drop. Z. Anal. Anwend. 16 (1997) 311-348
    • (1997) Z. Anal. Anwend. , vol.16 , pp. 311-348
    • Günther, M.1    Prokert, G.2
  • 18
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer, Berlin
    • Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. vol. 840 (1981), Springer, Berlin
    • (1981) Lecture Notes in Math. , vol.840
    • Henry, D.1
  • 19
    • 33846783056 scopus 로고    scopus 로고
    • Stable and unstable manifolds for quasilinear parabolic systems with fully nonlinear boundary conditions
    • Latushkin Y., Prüss J., and Schnaubelt R. Stable and unstable manifolds for quasilinear parabolic systems with fully nonlinear boundary conditions. J. Evol. Equ. 6 (2006) 537-576
    • (2006) J. Evol. Equ. , vol.6 , pp. 537-576
    • Latushkin, Y.1    Prüss, J.2    Schnaubelt, R.3
  • 20
    • 63449092028 scopus 로고    scopus 로고
    • Center manifolds and dynamics near equilibria for quasilinear parabolic systems with fully nonlinear boundary conditions
    • Latushkin Y., Prüss J., and Schnaubelt R. Center manifolds and dynamics near equilibria for quasilinear parabolic systems with fully nonlinear boundary conditions. Discrete Contin. Dyn. Syst. Ser. B 9 (2008) 595-633
    • (2008) Discrete Contin. Dyn. Syst. Ser. B , vol.9 , pp. 595-633
    • Latushkin, Y.1    Prüss, J.2    Schnaubelt, R.3
  • 21
    • 0003236729 scopus 로고
    • Analytic Semigroups and Optimal Regularity in Parabolic Problems
    • Birkhäuser, Basel
    • Lunardi A. Analytic Semigroups and Optimal Regularity in Parabolic Problems. Progr. Nonlinear Differential Equations Appl. vol. 16 (1995), Birkhäuser, Basel
    • (1995) Progr. Nonlinear Differential Equations Appl. , vol.16
    • Lunardi, A.1
  • 22
    • 0000387482 scopus 로고
    • Locally invariant manifolds for quasilinear parabolic equations
    • Mielke A. Locally invariant manifolds for quasilinear parabolic equations. Rocky Mountain J. Math. 21 (1991) 707-714
    • (1991) Rocky Mountain J. Math. , vol.21 , pp. 707-714
    • Mielke, A.1
  • 23
    • 0003334487 scopus 로고
    • Evolutionary Integral Equations and Applications
    • Birkhäuser, Basel
    • Prüss J. Evolutionary Integral Equations and Applications. Monogr. Math. vol. 87 (1993), Birkhäuser, Basel
    • (1993) Monogr. Math. , vol.87
    • Prüss, J.1
  • 25
    • 34249936488 scopus 로고    scopus 로고
    • Existence of analytic solutions for the classical Stefan problem
    • Prüss J., Saal J., and Simonett G. Existence of analytic solutions for the classical Stefan problem. Math. Ann. 338 (2007) 703-755
    • (2007) Math. Ann. , vol.338 , pp. 703-755
    • Prüss, J.1    Saal, J.2    Simonett, G.3
  • 26
    • 63449132975 scopus 로고    scopus 로고
    • Stability of equilibria for the Stefan problem with surface tension
    • Prüss J., and Simonett G. Stability of equilibria for the Stefan problem with surface tension. SIAM J. Math. Anal. 40 (2008) 675-698
    • (2008) SIAM J. Math. Anal. , vol.40 , pp. 675-698
    • Prüss, J.1    Simonett, G.2
  • 27
    • 63449117551 scopus 로고    scopus 로고
    • On normal stability for nonlinear parabolic equations
    • submitted for publication
    • J. Prüss, G. Simonett, R. Zacher, On normal stability for nonlinear parabolic equations, submitted for publication
    • Prüss, J.1    Simonett, G.2    Zacher, R.3
  • 28
    • 84972539057 scopus 로고
    • Center manifolds for quasilinear reaction-diffusion systems
    • Simonett G. Center manifolds for quasilinear reaction-diffusion systems. Differential Integral Equations 8 (1995) 753-796
    • (1995) Differential Integral Equations , vol.8 , pp. 753-796
    • Simonett, G.1
  • 29
    • 0000950086 scopus 로고
    • Center manifold theory in infinite dimensions
    • Dynamics Reported: Expositions in Dynamical Systems, Springer, Berlin
    • Vanderbauwhede A., and Iooss G. Center manifold theory in infinite dimensions. Dynamics Reported: Expositions in Dynamical Systems. Dynam. Report. Expositions Dynam. Systems (N.S.) vol. 1 (1992), Springer, Berlin 125-163
    • (1992) Dynam. Report. Expositions Dynam. Systems (N.S.) , vol.1 , pp. 125-163
    • Vanderbauwhede, A.1    Iooss, G.2


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