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Attractors of the non-autonomous reaction-diffusion equation with nonlinear boundary condition. (English) Zbl 1201.35054
Summary: We study the long-time behavior of the non-autonomous reaction-diffusion equation with nonlinear boundary condition and competing nonlinearities. Under balance conditions between internal and boundary nonlinear terms, we prove the existence of a compact uniform attractor in $L^{p+1}(\Omega )$ where $p>1$ is the growing exponent of internal nonlinearity.

MSC:
35B41Attractors (PDE)
35K61Nonlinear parabolic equations, nonlinear initial boundary value problems
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References:
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