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, IranJorge Ferreira
Federal Fluminense University, Rio de Janeiro, BrazilFaramarz Tahamtani
Shiraz University, Iran
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