On the time-dependent Cattaneo law in space dimension one

Monica Conti and Vittorino Pata

Applied Mathematics and Computation, 2015, vol. 259, issue C, 32-44

Abstract: We consider the one-dimensional wave equationεutt-uxx+[1+εf′(u)]ut+f(u)=hwhere ε=ε(t) is a decreasing function vanishing at infinity, providing a model for heat conduction of Cattaneo type with thermal resistance decreasing in time. Within the theory of processes on time-dependent spaces, we prove the existence of an invariant time-dependent attractor, which converges in a suitable sense to the attractor of the classical Fourier equationut-uxx+f(u)=hformally arising in the limit t→∞.

Keywords: Cattaneo law; Nonautonomous dynamical systems; Wave equation; Time-dependent attractors (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:259:y:2015:i:c:p:32-44

DOI: 10.1016/j.amc.2015.02.039

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