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arXiv · 1503.05744

Long-term behavior of reaction-diffusion equations with nonlocal boundary conditions on rough domains

Ciprian G. Gal·Mahamadi Warma
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Abstract

We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin boundary conditions, characterized by the presence of fractional diffusion on the boundary. Our results are of general character and apply to a large class of irregular domains, including domains whose boundary is Holder continuous and domains which have fractal-like geometry. In addition to recovering most of the existing results on existence, regularity, uniqueness, stability, attractor existence, and dimension, for the well-known reaction-diffusion equation in smooth domains, the framework we develop also makes possible a number of new results for all diffusion models in other non-smooth settings.

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Ciprian G. Gal, Mahamadi Warma. 2015-03-19. Long-term behavior of reaction-diffusion equations with nonlocal boundary conditions on rough domains. https://doi.org/10.1007/s00033-016-0673-8

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