Reaction-diffusion with memory in the minimal state framework

Conti, Monica; Marchini, Elsa; Pata, Vittorino

doi:10.1090/S0002-9947-2013-06097-7

Reaction-diffusion with memory in the minimal state framework
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by Monica Conti, Elsa M. Marchini and Vittorino Pata PDF

Trans. Amer. Math. Soc. 366 (2014), 4969-4986 Request permission

Abstract:

We consider the integrodifferential equation \[ \partial _t u-\Delta u -\int _0^\infty \kappa (s)\Delta u(t-s) \mathrm {d} s + \varphi (u)=f\] arising in the Coleman-Gurtin theory of heat conduction with hereditary memory. Within a novel abstract framework, based on the notion of minimal state, we prove the existence of global and exponential attractors of optimal regularity and finite fractal dimension for the related semigroup of solutions.

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