General decay result for nonlinear viscoelastic equations |
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Authors: | Muhammad I. Mustafa |
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Affiliation: | Department of Mathematics, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates |
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Abstract: | In this paper we consider a nonlinear viscoelastic equation with minimal conditions on the relaxation function g namely , where H is an increasing and convex function near the origin and ξ is a nonincreasing function. With only these very general assumptions on the behavior of g at infinity, we establish optimal explicit and general energy decay results from which we can recover the optimal exponential and polynomial rates when and p covers the full admissible range . We get the best decay rates expected under this level of generality and our new results substantially improve several earlier related results in the literature. |
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Keywords: | General decay Viscoelastic damping Relaxation function Convexity |
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