Uniform attractors for a non-autonomous semilinear heat equation with memory

Authors:
Claudio Giorgi, Vittorino Pata and Alfredo Marzocchi

Journal:
Quart. Appl. Math. **58** (2000), 661-683

MSC:
Primary 37L30; Secondary 35B41, 35K57, 35R10, 45K05

DOI:
https://doi.org/10.1090/qam/1788423

MathSciNet review:
MR1788423

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Abstract: In this paper we investigate the asymptotic behavior, as time tends to infinity, of the solutions of a non-autonomous integro-partial differential equation describing the heat flow in a rigid heat conductor with memory. Existence and uniqueness of solutions is provided. Moreover, under proper assumptions on the heat flux memory kernel and on the magnitude of nonlinearity, the existence of uniform absorbing sets and of a global uniform attractor is achieved. In the case of quasiperiodic dependence of time of the external heat supply, the above attractor is shown to have finite Hausdorff dimension.

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DOI:
https://doi.org/10.1090/qam/1788423

Article copyright:
© Copyright 2000
American Mathematical Society