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Dynamics of the viscous Cahn-Hilliard equation

Carvalho, A. N.; Dlotko, Tomasz Universidade De São Paulo

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.344, n.2, p.703-725, 2008

ACADEMIC PRESS INC ELSEVIER SCIENCE 2008

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  • Título:
    Dynamics of the viscous Cahn-Hilliard equation
  • Autor: Carvalho, A. N.; Dlotko, Tomasz
  • Universidade De São Paulo
  • Assuntos: Viscous Cahn-Hilliard Equation; Global Attractor; Attractors; Lower Semicontinuity; Critical Nonlinearities; Global Attractors; Wave-Equations; Perturbations; Mathematics; Applied; Mathematics
  • É parte de: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.344, n.2, p.703-725, 2008
  • Descrição: We study generalized viscous Cahn-Hilliard problems with nonlinearities satisfying critical growth conditions in W-0(1,p)(Omega), where Omega is a bounded smooth domain in R-n, n >= 3. In the critical growth case, we prove that the problems are locally well posed and obtain a bootstrapping procedure showing that the solutions are classical. For p = 2 and almost critical dissipative nonlinearities we prove global well posedness, existence of global attractors in H-0(1)(Omega) and, uniformly with respect to the viscosity parameter, L-infinity(Omega) bounds for the attractors. Finally, we obtain a result on continuity of regular attractors which shows that, if n = 3, 4, the attractor of the Cahn-Hilliard problem coincides (in a sense to be specified) with the attractor for the corresponding semilinear heat equation. (C) 2008 Elsevier Inc. All rights reserved.
  • DOI: 10.1016/j.jmaa.2008.03.020
  • Títulos relacionados: Journal of Mathematical Analysis and Applications
  • Editor: ACADEMIC PRESS INC ELSEVIER SCIENCE
  • Data de publicação: 2008
  • Idioma: Inglês
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  • Realização: USP

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