NEW GENERAL DECAY RATES OF SOLUTIONS FOR TWO VISCOELASTIC WAVE EQUATIONS WITH INFINITE MEMORY | Zendy

Aı̈ssa Guesmia | Zendy

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NEW GENERAL DECAY RATES OF SOLUTIONS FOR TWO VISCOELASTIC WAVE EQUATIONS WITH INFINITE MEMORY

Author(s) -

Aı̈ssa Guesmia

Publication year - 2020

Publication title -

mathematical modelling and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.491

H-Index - 25

eISSN - 1648-3510

pISSN - 1392-6292

DOI - 10.3846/mma.2020.10458

Subject(s) - infinity , viscoelasticity , mathematics , exponential stability , wave equation , mathematical analysis , stability (learning theory) , class (philosophy) , long memory , physics , computer science , thermodynamics , nonlinear system , quantum mechanics , machine learning , artificial intelligence , volatility (finance) , econometrics

We consider in this paper the problem of asymptotic behavior of solutions for two viscoelastic wave equations with infinite memory. We show that the stability of the system holds for a much larger class of kernels and get better decay rate than the ones known in the literature. More precisely, we consider infinite memory kernels satisfying, where and are given functions. Under this very general assumption on the behavior of g at infinity and for each viscoelastic wave equation, we provide a relation between the decay rate of the solutions and the growth of g at infinity, which improves the decay rates obtained in [15, 16, 17, 19, 40]. Moreover, we drop the boundedness assumptions on the history data considered in [15, 16, 17, 40].

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