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Sup-norm estimates for parabolic systems with dynamic boundary conditions (1210.7671v1)
Published 29 Oct 2012 in math.AP and math.DS
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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