Differential and Integral Equations
- Differential Integral Equations
- Volume 23, Number 3/4 (2010), 327-358.
Well posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions
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.
Differential Integral Equations, Volume 23, Number 3/4 (2010), 327-358.
First available in Project Euclid: 20 December 2012
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Gal, Ciprian G.; Warma, Mahamadi. Well posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions. Differential Integral Equations 23 (2010), no. 3/4, 327--358. https://projecteuclid.org/euclid.die/1356019321