Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774656 | Journal of Mathematical Analysis and Applications | 2018 | 19 Pages |
Abstract
In this paper we consider a nonlinear viscoelastic equation with minimal conditions on the L1(0,â) relaxation function g namely gâ²(t)â¤âξ(t)H(g(t)), 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 H(s)=sp and p covers the full admissible range [1,2). 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Muhammad I. Mustafa,