On a class of degenerate parabolic equations with dynamic boundary conditions
By Ciprian G. Gal. 2011
62 citations recorded by the source corpus.
We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of initial and boundary value problems has already been studied previously, proving well-posedness and the existence of the global attractor. The goal of this note is to show that the previous analysis can be redone for more general nonlinearities by proving an additional (uniform) L\infty-estimate on the solutions. In particular, we derive new conditions which reflect an exact balance between the two nonlinear mechanisms involved, even when both the nonlinear (source) terms contribute in opposite directions.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fd2ae74cfe0aab3c20c9703a45921c5cd6c365ce
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In Computational Theory and Mathematics
- Hao Wu
- Maurizio Grasselli
- Ciprian G. Gal
- Alain Miranville
- Laurence Cherfils
- Sergey Zelik
- David E. V. Rose
In Control and Systems Engineering
In Mathematical Physics
Citations in the corpus
- Longtime behavior of nonlocal Cahn-Hilliard equations (2012, background): “10) relies on an iterative argument as in [24].”
- A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, background): “, heat conduction with heat source on the boundary, kinetic motion on the boundary of a vibrating object etc) and have been extensively analyzed in the literature, see for instance, [4, 7, 50,54,61,62,70,89,97,103,123,166,175,179] and the references cited therein.”