Asymptotic behavior of a semilinear problem in heat conduction with memory. (English) Zbl 0912.45009
The authors investigate the existence, uniqueness, and asymptotic properties of solutions to a Volterra integro-differential equation arising in the mathematical modeling of heat flow in materials with memory. The existence-uniqueness theory is developed with the help of a Faedo-Galerkin scheme. The key result in the study of long time behavior of solutions is a theorem establishing the existence of absorbing sets in a suitable weighted Hilbert space.
Reviewer: S.Aizicovici (Athens/Ohio)
MSC:
45K05 | Integro-partial differential equations |
45M05 | Asymptotics of solutions to integral equations |