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

Author

Listed:
  • 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
    Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Turkey)

  • 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)

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.

Suggested Citation

  • Bochra Belhadji & Jehad Alzabut & Mohammad Esmael Samei & Nahid Fatima, 2022. "On the Global Behaviour of Solutions for a Delayed Viscoelastic-Type Petrovesky Wave Equation with p -Laplacian Operator and Logarithmic Source," Mathematics, MDPI, vol. 10(22), pages 1-39, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4194-:d:968005
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