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Almost periodicity of all \(L^2\)-bounded solutions of a functional heat equation. (English) Zbl 1450.35130
The aim of this paper is study the existence of almost periodic solutions for some reaction-diffusion equations with delay. The authors prove that each \(L^2\)-bounded solution on \(\mathbb R\) is almost periodic. The linear part is given by the Laplacian operator on a smooth domain, the nonlinear part is assumed to be Lipschitzian and almost periodic in \( t\).
MSC:
35K05 Heat equation
35B15 Almost and pseudo-almost periodic solutions to PDEs
35R10 Functional partial differential equations
35K57 Reaction-diffusion equations
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References:
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