Existence and Qualitative Properties of Solution for a Class of Nonlinear Wave Equations with Delay Term and Variable-Exponents Nonlinearities
Mohamed Karek,
Sadok Otmani,
Keltoum Bouhali,
Khaled Zennir,
Hatim M. Elkhair,
Eltegani I. Hassan,
Alnadhief H. A. Alfedeel,
Almonther Alarfaj
Affiliations
Mohamed Karek
Department of Earth Science, Faculty of Hydrocarbons and Earth Science and Renewable Energies, University of Kasdi Merbah Ouargla, Ouargla 30000, Algeria
Sadok Otmani
Department of Mathematics, Faculty of Science, University of Kasdi Merbah Ouargla, Ouargla 30000, Algeria
Keltoum Bouhali
Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51452, Saudi Arabia
Khaled Zennir
Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51452, Saudi Arabia
Hatim M. Elkhair
Deanship of Scientific Research, Imam Mohammad Ibn Saud Islamic University, P. O. Box 5701, Riyadh 11432, Saudi Arabia
Eltegani I. Hassan
Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
Alnadhief H. A. Alfedeel
Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
Almonther Alarfaj
Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
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.
