We consider the nonclassical diffusion equation with hereditary memory (Formula Presented) on a bounded three-dimensional domain. The main feature of the model is that the equation does not contain a term of the form −∆u, contributing as an instantaneous damping. Setting the problem in the past history framework, we prove that the related solution semigroup possesses a global attractor of optimal regularity.
Nonclassical diffusion with memory lacking instantaneous damping
Conti M.;Dell'Oro F.;Pata V.
2020-01-01
Abstract
We consider the nonclassical diffusion equation with hereditary memory (Formula Presented) on a bounded three-dimensional domain. The main feature of the model is that the equation does not contain a term of the form −∆u, contributing as an instantaneous damping. Setting the problem in the past history framework, we prove that the related solution semigroup possesses a global attractor of optimal regularity.File in questo prodotto:
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