Blow-up of solutions to a viscoelastic wave equation with nonlocal damping

Donghao Li; Hongwei Zhang; Shuo Liu; Qingiyng Hu

doi:10.3934/eect.2022009

Article Contents

2022, Volume 11, Issue 6: 2017-2031. Doi: 10.3934/eect.2022009

This issue Previous Article Exponential stability and stabilization of fractional stochastic degenerate evolution equations in a Hilbert space: Subordination principle Next Article Controller and asymptotic autonomy of random attractors for stochastic p-Laplace lattice equations

Blow-up of solutions to a viscoelastic wave equation with nonlocal damping

Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China

^* Corresponding author: Hongwei Zhang
^* Corresponding author: Hongwei Zhang

Received: August 2021

Revised: December 2021

Early access: February 2022

Published: December 2022

This work is supported by National Natural Science Foundation of China (No.11801145) and the Innovative Funds Plan of Henan University of Technology (2020ZKCJ09).

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Abstract

The viscoelastic wave equation with nonlinear nonlocal weak damping is considered. The local existence of solutions is established. Under arbitrary positive initial energy, a finite-time blow-up result is proved by a new modified concavity method.

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Mathematics Subject Classification: Primary: 35L05, 35L20, 35B44.

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