On the Global Behaviour of Solutions for a Delayed Viscoelastic-Type Petrovesky Wave Equation with p -Laplacian Operator and Logarithmic Source

Bochra Belhadji, Jehad Alzabut (), Mohammad Esmael Samei and Nahid Fatima
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Bochra Belhadji: Laboratoire de Mathématiques et Sciences Appliquées, Université de Ghardaia, Ghardaia 47000, Algeria
Jehad Alzabut: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Mohammad Esmael Samei: Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan 65178, Iran
Nahid Fatima: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Mathematics, 2022, vol. 10, issue 22, 1-39

Abstract: This research is concerned with a nonlinear p -Laplacian-type wave equation with a strong damping and logarithmic source term under the null Dirichlet boundary condition. We establish the global existence of the solutions by using the potential well method. Moreover, we prove the stability of the solutions by the Nakao technique. An example with illustrative figures is provided as an application.

Keywords: global existence; energy decay; viscoelastic wave equation; strong damping; p -Laplacian; logarithmic nonlinearity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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