Reaction-diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions. (English) Zbl 1334.35387
Summary: 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.
MSC:
| 35R11 | Fractional partial differential equations |
| 35A15 | Variational methods applied to PDEs |
| 35B41 | Attractors |
| 35K65 | Degenerate parabolic equations |
| 35K57 | Reaction-diffusion equations |
Keywords:
fractional Laplace operator; fractional Neumann and Robin boundary conditions on open sets; global attractor; convergence to steady states; semi-linear reaction-diffusion equation; asymptotic behaviorReferences:
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