n 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 how 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.

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

GIORGI, Claudio;MARZOCCHI, Alfredo;PATA, Vittorino
2000-01-01

Abstract

n 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 how 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/20031
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