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arXiv · 1210.7671

Sup-norm estimates for parabolic systems with dynamic boundary conditions

Ciprian G. Gal
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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.

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Ciprian G. Gal. 2012-10-29. Sup-norm estimates for parabolic systems with dynamic boundary conditions. https://arxiv.org/abs/1210.7671

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