GLOBAL ATTRACTORS FOR A NONCLASSICAL DIFFUSION EQUATION LACKING INSTANTANEOUS DAMPING WITH MEMORY
Keywords:
Nonclassical diffusion; lacking instantaneous damping; memory; global attractor; semigroupAbstract
In this paper, we consider a periodic boundary value problem for a nonclassical diffusion equation lacking instantaneous damping with hereditary memory ut −∆ut −Z∞ 0 κ(s)∆u(t−s)ds + k0|u|p−1u = g. The main characteristics of the model is that the equation does not contain a term of the form −∆u, which contributes to an instantaneous damping. We use the ω-limit compactness of the solution semigroup {S(t)}t≥0 to get the existence of a global attractor.
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