Jieqiong Wu, Fei Feng, Shugen Chai
Abstract:
We study the energy decay for the Cauchy problem of the wave equation with
nonlinear time-dependent and space-dependent damping.
The damping is localized in a bounded domain and near infinity, and
the principal part of the wave equation has a variable-coefficient.
We apply the multiplier method for variable-coefficient equations, and
obtain an energy decay that depends on the property of the coefficient
of the damping term.
Submitted May 28, 2015. Published September 2, 2015.
Math Subject Classifications: 35L05, 35L70, 93B27.
Key Words: Energy decay; time-dependent and space-dependent damping;
localized damping; Riemannian geometry method; variable coefficient.
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Jieqiong Wu School of Mathematical Sciences Shanxi University Taiyuan, Shanxi 030006, China email: jieqiong@sxu.edu.cn |
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Fei Feng School of Mathematical Sciences Shanxi University Taiyuan, Shanxi 030006, China email: fengfei599@126.com |
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Shugen Chai School of Mathematical Sciences Shanxi University Taiyuan, Shanxi 030006, China email: sgchai@sxu.edu.cn |
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