Well posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions

@article{Gal2010WellPA,
  title={Well posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions},
  author={Ciprian G. Gal and Mahamadi Warma},
  journal={Differential and Integral Equations},
  year={2010}
}
  • C. GalM. Warma
  • Published 1 March 2010
  • Mathematics
  • Differential and Integral Equations
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… 
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