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Nonexistence of global solutions to wave Equations with structural damping and nonlinear memory
  • Mokhtar Kirane,
  • Abderrazak NABTi,
  • Mohamed Jleli
Mokhtar Kirane
University de La Rochelle
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Abderrazak NABTi
Universite de Tebessa
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Mohamed Jleli
kING SAUD UNIVERSITY Riyadh, Saudi Arabia
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For the following wave equations with structural damping and nonlinear memory source terms \[ u_{tt}+(-\Delta)^{\frac{\alpha}{2}}u +(-\Delta)^{\frac{\beta}{2}}u_t =\int_{0}^{t}(t-s)^{\gamma-1} \vert u (s)\vert^{p}\,\text{d}s, \] and \[ u_{tt}+(-\Delta)^{\frac{\alpha}{2}}u +(-\Delta)^{\frac{\beta}{2}}u_t = \int_{0}^{t}(t-s)^{\gamma-1} \vert u_s (s)\vert^{p}\,\text{d}s, \] posed in $(x,t) \in \mathbb{R}^N \times [0,\infty) $, where $u=u(x,t)$ is real-value unknown function, $p>1$, $\alpha,\beta\in (0, 2]$, $\gamma\in (0,1)$, we prove the nonexistence of global solutions. Moreover, we give an upper bound estimate of the life span of solutions.

Peer review status:UNDER REVIEW

25 Jun 2020Submitted to Mathematical Methods in the Applied Sciences
04 Jul 2020Submission Checks Completed
04 Jul 2020Assigned to Editor
07 Jul 2020Reviewer(s) Assigned
29 Sep 2020Review(s) Completed, Editorial Evaluation Pending
29 Sep 2020Editorial Decision: Revise Major
10 Apr 20211st Revision Received
10 Apr 2021Submission Checks Completed
10 Apr 2021Assigned to Editor
20 Apr 2021Reviewer(s) Assigned