Reaction-diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions

Ciprian G. Gal; Mahamadi Warma

doi:10.3934/dcds.2016.36.1279

Article Contents

2016, Volume 36, Issue 3: 1279-1319. Doi: 10.3934/dcds.2016.36.1279

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Reaction-diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions

Ciprian G. Gal^1, and
Mahamadi Warma^2,

1.
Department of Mathematics, Florida International University, Miami, FL, 33199
2.
University of Puerto Rico, Rio Piedras Campus, Department of Mathematics, P.O. Box 70377, San Juan PR 00936-8377

Received: October 31, 2014

Revised: February 28, 2015

Published: May 2017

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Abstract

We investigate the long term behavior in terms of finite dimensional global attractors and (global) asymptotic stabilization to steady states, as time goes to infinity, of solutions to a non-local semilinear reaction-diffusion equation associated with the fractional Laplace operator on non-smooth domains subject to Dirichlet, fractional Neumann and Robin boundary conditions.

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Mathematics Subject Classification: 35R11, 35A15, 35B41, 35K65.

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