International Journal of Nonlinear Analysis and Applications

Existence, asymptotic stability and blow-up results for a variable-exponent viscoelastic double-Kirchhoff-type wave equation

Document Type : Research Paper

Authors

1 Department of Mathematics, Jahrom University, Jahrom, Iran

2 Federal Fluminense University, Department of Exact Sciences, Volta Redonda, RJ, Brazil

3 Dicle University, Department of Mathematics, Diyarbakir, Turkey

Abstract

The present study examined the behavior of solutions for a viscoelastic double-Kirchhoff-type wave equation with nonlocal degenerate damping term and variable exponent nonlinearities. Under appropriate conditions for the data and exponents, we prove the global existence, asymptotic stability, and blow up of solutions with arbitrary initial energy.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 2
February 2024
Pages 95-114
  • Receive Date: 12 November 2022
  • Revise Date: 27 December 2022
  • Accept Date: 06 March 2023