Optimal decay rates for the abstract viscoelastic equation View Full Text


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Article Info

DATE

2019-02-08

AUTHORS

Muhammad I. Mustafa

ABSTRACT

In this paper, we consider an abstract viscoelastic equation with minimal conditions on the L1(0,∞) relaxation function g namely g′(t)≤-ξ(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. More... »

PAGES

1-17

References to SciGraph publications

  • 2014. Intrinsic Decay Rate Estimates for Semilinear Abstract Second Order Equations with Memory in NEW PROSPECTS IN DIRECT, INVERSE AND CONTROL PROBLEMS FOR EVOLUTION EQUATIONS
  • 1996-04. Decay rates of solutions of an anisotropic inhomogeneousn-dimensional viscoelastic equation with polynomially decaying kernels in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1989. Mathematical Methods of Classical Mechanics in NONE
  • 2016-01. Uniform Decay Rates for Viscoelastic Dissipative Systems in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 1970-01. Asymptotic stability in viscoelasticity in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
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    http://scigraph.springernature.com/pub.10.1007/s00028-019-00488-7

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