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March/April 2010 Well posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions
Ciprian G. Gal, Mahamadi Warma
Differential Integral Equations 23(3/4): 327-358 (March/April 2010).

Abstract

We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as generalizations of semilinear reaction-diffusion equations with dynamic boundary conditions and various other phase-field models, such as the isothermal Allen-Cahn equation with dynamic boundary conditions. We thus formulate a class of initial and boundary-value problems whose global existence and uniqueness is proven by means of an appropriate Faedo-Galerkin approximation scheme developed for problems with dynamic boundary conditions. We analyze the asymptotic behavior of the solutions within the theory of infinite-dimensional dynamical systems. In particular, we demonstrate the existence of the global attractor.

Citation

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Ciprian G. Gal. Mahamadi Warma. "Well posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions." Differential Integral Equations 23 (3/4) 327 - 358, March/April 2010.

Information

Published: March/April 2010
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35307
MathSciNet: MR2588479

Subjects:
Primary: 35B41, 35K55, 37L30, 80A22

Rights: Copyright © 2010 Khayyam Publishing, Inc.

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Vol.23 • No. 3/4 • March/April 2010
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