Sup-norm estimates for parabolic systems with dynamic boundary conditions
Analysis of PDEs
2012-10-30 v1 Dynamical Systems
Abstract
We consider parabolic systems with nonlinear dynamic boundary conditions, for which we give a rigorous derivation. Then, we give them several physical interpretations which includes an interpretation for the porous-medium equation, and for certain reaction-diffusion systems that occur in mathematical biology and ecology. We devise several strategies which imply (uniform)}L^{p} and}L^{\infty}$ estimates on the solutions for the initial value problems considered.
Cite
@article{arxiv.1210.7671,
title = {Sup-norm estimates for parabolic systems with dynamic boundary conditions},
author = {Ciprian G. Gal},
journal= {arXiv preprint arXiv:1210.7671},
year = {2012}
}