Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping
Joint Authors
Source
Advances in Mathematical Physics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-05-06
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We are concerned in this paper with the initial boundary value problem for a quasilinear viscoelastic wave equation which is subject to a nonlinear action, to a nonlinear frictional damping, and to a Kelvin-Voigt damping, simultaneously.
By utilizing a carefully chosen Lyapunov functional, we establish first by the celebrated convexity argument a finite time blow-up criterion for the initial boundary value problem in question; we prove second by an a priori estimate argument that some solutions to the problem exists globally if the nonlinearity is “weaker,” in a certain sense, than the frictional damping, and if the viscoelastic damping is sufficiently strong.
American Psychological Association (APA)
Wang, Fosheng& Wang, Chengqiang. 2018. Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping. Advances in Mathematical Physics،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1119318
Modern Language Association (MLA)
Wang, Fosheng& Wang, Chengqiang. Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping. Advances in Mathematical Physics No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1119318
American Medical Association (AMA)
Wang, Fosheng& Wang, Chengqiang. Blow-Up and Global Existence Analysis for the Viscoelastic Wave Equation with a Frictional and a Kelvin-Voigt Damping. Advances in Mathematical Physics. 2018. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1119318
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119318