Theoretical and computational decay results for a memory type wave equation with variable-exponent nonlinearity | Zendy

Adel M. AlMahdi | Zendy; Mohammad M. AlGharabli | Zendy; Mostafa Zahri | Zendy

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Theoretical and computational decay results for a memory type wave equation with variable-exponent nonlinearity

Author(s) -

Adel M. AlMahdi,

Mohammad M. AlGharabli,

Mostafa Zahri

Publication year - 2022

Publication title -

mathematical control and related fields

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.658

H-Index - 21

eISSN - 2156-8472

pISSN - 2156-8499

DOI - 10.3934/mcrf.2022010

Subject(s) - exponent , constraint (computer aided design) , type (biology) , relaxation (psychology) , variable (mathematics) , mathematics , nonlinear system , viscoelasticity , function (biology) , mathematical analysis , wave equation , statistical physics , physics , quantum mechanics , thermodynamics , geometry , psychology , ecology , social psychology , philosophy , linguistics , evolutionary biology , biology

In this paper we are concerned with a viscoelastic wave equation with infinite memory and nonlinear frictional damping of variable-exponent type. First, we establish explicit and general decay results with a very general assumption on the relaxation function. Then, we remove the constraint imposed on the boundedness condition on the initial data used in the earlier results in the literature. Finally, we perform several numerical tests to illustrate our theoretical findings. This study generalizes and improves previous literature outcomes.

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