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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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