On the time-dependent Cattaneo law in space dimension one

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摘要

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→∞.

论文关键词:Cattaneo law,Nonautonomous dynamical systems,Wave equation,Time-dependent attractors

论文评审过程:Available online 7 March 2015.

论文官网地址:https://doi.org/10.1016/j.amc.2015.02.039