Existence and Qualitative Properties of Solution for a Class of Nonlinear Wave Equations with Delay Term and Variable-Exponents Nonlinearities-Reference-Cited by-同舟云学术

Existence and Qualitative Properties of Solution for a Class of Nonlinear Wave Equations with Delay Term and Variable-Exponents Nonlinearities

Published:2023-04-30 Issue:5 Volume:12 Page:444
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Karek Mohamed¹,Otmani Sadok²,Bouhali Keltoum³⁴^ORCID,Zennir Khaled³,Elkhair Hatim M.⁵,Hassan Eltegani I.⁶,Alfedeel Alnadhief H. A.⁶,Alarfaj Almonther⁶

Affiliation:

1. Department of Earth Science, Faculty of Hydrocarbons and Earth Science and Renewable Energies, University of Kasdi Merbah Ouargla, Ouargla 30000, Algeria

2. Department of Mathematics, Faculty of Science, University of Kasdi Merbah Ouargla, Ouargla 30000, Algeria

3. Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51452, Saudi Arabia

4. Department of Mathematics, College of Sciences, Université 20 Août 1955 Skikda Bp 26 Route El-Hadaiek, Skikda 21000, Algeria

5. Deanship of Scientific Research, Imam Mohammad Ibn Saud Islamic University, P. O. Box 5701, Riyadh 11432, Saudi Arabia

6. Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia

Abstract

This article is devoted to a study of the question of existence (in time) of weak solutions and the derivation of qualitative properties of such solutions for the nonlinear viscoelastic wave equation with variable exponents and minor damping terms. By using the energy method combined with the Faedo–Galerkin method, the local and global existence of solutions are established. Then, the stability estimate of the solution is obtained by introducing a suitable Lyapunov function.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/5/444/pdf

Reference14 articles.

1. Energy decay of solutions for a wave equation with a constant weak delay and a weak internal feedback;Benaissa;Electron. J. Qual. Theory Differ. Equ.,2014

2. Energy decay for viscoelastic plates with distributed delay and source term;Mustafa;Z. Angew. Math. Phys.,2016

3. Nonlinear damped wave equation: Existence and blow-up;Messaoudi;Comput. Math. Appl.,2017

4. A blow-up result for nonlinear generalized heat equation;Kbiri;Comput. Math. Appl.,2014

5. Wave equation with p(x, t)-laplacian and damping term: Existence and blow-up;Antontsev;Differ. Equ. Appl.,2011