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Decay properties for the solutions of a partial differential equation with memory

Research paper by Jan Prüss

Indexed on: 11 Feb '09Published on: 11 Feb '09Published in: Archiv der Mathematik



Abstract

Decay properties in energy norm for solutions of a class of partial differential equations with memory are studied by means of frequency domain methods. Our results are optimal for this class, as we are able to characterize polynomial as well as exponential decay rates. The results apply to models for viscoelastic materials. An extension to a semilinearly perturbed problem is also included.