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

Claudio Giorgi, Vittorino Pata, Alfredo Marzocchi
2000 Quarterly of Applied Mathematics  
In this paper we investigate the asymptotic behavior, as time tends to infinity, of the solutions of an 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 case of quasiperiodic dependence
more » ... eriodic dependence of time of the external heat supply, the above attractor is shown to have finite Hausdorff dimension. x ∈ Ω (0.1) AMS subject classifications. 35B40, 35K05, 45K05, 47H20.
doi:10.1090/qam/1788423 fatcat:hqlwuwtfevfg5jozhwe5tcubky