Exponential decay and blow-up results for a viscoelastic equation with variable sources

This work deals with a class of nonlinear viscoelastic wave equations with strong damping and variable exponent sources. The main interest of this paper compared to many previous works in the literature is able to use the idea of potential well method to study both the finite time blow-up for soluti...

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Bibliographic Details
Published inApplicable analysis Vol. 102; no. 3; pp. 782 - 799
Main Authors Le, Nhan Cong, Le, Truong Xuan, Nguyen, Y. Van
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 11.02.2023
Taylor & Francis Ltd
Subjects
74Dxx
blow-up
Damping
Decay
decay estimate
Nonlinear wave equation
variable exponent sources
Viscoelasticity
Wave equations
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Summary:This work deals with a class of nonlinear viscoelastic wave equations with strong damping and variable exponent sources. The main interest of this paper compared to many previous works in the literature is able to use the idea of potential well method to study both the finite time blow-up for solutions starting from the unstable sets and decay estimate for global solutions starting in the potential wells.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2021.1965581