Xiaoying Zhang, Shugen Chai, Jieqiong Wu
Abstract:
We study the blow-up of the solution to a quasilinear viscoelastic wave
system coupled by nonlinear sources. The system is of
homogeneous Dirichlet boundary condition. The nonlinear damping and source
are added to the equations. We assume that the relaxation functions
are non-negative non-increasing functions and the initial energy is
negative. The competition relations among the nonlinear principal parts
are not constant functions, the viscoelasticity terms, dampings and
sources are analyzed by using perturbed energy method.
The blow-up result is proved under some conditions on the nonlinear principal
parts, viscoelasticity terms, dampings and sources by a contradiction argument.
Submitted February 26, 2016. Published March 21, 2017.
Math Subject Classifications: 35A01, 35L53.
Key Words: Blow up; quasilinear wave system; viscoelasticity.
Show me the PDF file (216 KB), TEX file for this article.
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Xiaoying Zhang School of Mathmatical Sciences Shanxi University Taiyuan, Shanxi 030006, China email: zxybetter@163.com |
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Shugen Chai School of Mathmatical Sciences Shanxi University Taiyuan, Shanxi 030006, China email: sgchai@sxu.edu.cn |
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Jieqiong Wu School of Mathmatical Sciences Shanxi University Taiyuan, Shanxi 030006, China email: jieqiong@sxu.edu.cn |
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