Global existence, asymptotic stability and blow up of solutions for a nonlinear viscoelastic plate equation involving (p(x), q(x))-Laplacian operator

  • Mohammad Shahrouzi

    Jahrom University, Iran
  • Jorge Ferreira

    Federal Fluminense University, Rio de Janeiro, Brazil
  • Faramarz Tahamtani

    Shiraz University, Iran
Global existence, asymptotic stability and blow up of solutions for a nonlinear viscoelastic plate equation involving (p(x), q(x))-Laplacian operator cover

A subscription is required to access this article.

Abstract

This study aims at investigating the global existence, asymptotic stability and blow up of solutions for a nonlinear viscoelastic fourth-order (p(x), q(x))-Laplacian equation with variable-exponent nonlinearities. First, we prove the global existence of solutions, and next, we show that the solutions are asymptotically stable if initial data p(x) and q(x) are in the appropriate range. Moreover, under suitable conditions on initial data, we prove that there exists a finite time in which some solutions blow up with positive as well as negative initial energies.

Cite this article

Mohammad Shahrouzi, Jorge Ferreira, Faramarz Tahamtani, Global existence, asymptotic stability and blow up of solutions for a nonlinear viscoelastic plate equation involving (p(x), q(x))-Laplacian operator. Z. Anal. Anwend. 42 (2023), no. 1/2, pp. 91–115

DOI 10.4171/ZAA/1722