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arXiv · 1302.4265

Hyperbolic Relaxation of Reaction Diffusion Equations with Dynamic Boundary Conditions

Ciprian G. Gal·Joseph L. Shomberg
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Abstract

Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary condition. Each problem is well-posed in a suitable phase space where the global weak solutions generate a Lipschitz continuous semiflow which admits a bounded absorbing set. We prove the existence of a family of global attractors of optimal regularity. After fitting both problems into a common framework, a proof of the upper-semicontinuity of the family of global attractors is given as the relaxation parameter goes to zero. Finally, we also establish the existence of exponential attractors.

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Ciprian G. Gal, Joseph L. Shomberg. 2013-02-18. Hyperbolic Relaxation of Reaction Diffusion Equations with Dynamic Boundary Conditions. https://arxiv.org/abs/1302.4265

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