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\(H^{2}\)-boundedness of the pullback attractor for a non-autonomous reaction-diffusion equation. (English) Zbl 1180.35117

Summary: We prove some regularity results for the pullback attractor of a reaction-diffusion model. First, we establish a general result about \(H^{2}\)-boundedness of invariant sets for an evolution process. Then, as a consequence, we deduce that the pullback attractor of a non-autonomous reaction-diffusion equation is bounded not only in \(L^2(\varOmega)\cap H_0^1 (\varOmega)\) but also in \(H^{2}(\Omega )\).

MSC:

35B41 Attractors
35Q35 PDEs in connection with fluid mechanics
35K57 Reaction-diffusion equations
35K58 Semilinear parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
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