Spatial Asymptotic Properties of a System Wave Equations with Nonlinear Damping and Source Terms

doi:10.13371/j.cnki.chin.q.j.m.2021.01.005

Chinese Quarterly Journal of Mathematics ›› 2021, Vol. 36 ›› Issue (1): 67-78.doi: 10.13371/j.cnki.chin.q.j.m.2021.01.005

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Spatial Asymptotic Properties of a System Wave Equations with Nonlinear Damping and Source Terms

Department of Apllied Mathematics, Huashang College Guangdong University of Finance & Economics,

Received:2020-11-26 Online:2021-03-30 Published:2021-03-30
About author: LI Yuan-fei (1982-), male, native of Guangdong, Guangzhou, distinguished professor of Huashang College Guangdong University of Finance & Economics, engages in partial differential equation.
Supported by:
Supported by Innovation Team Project of Humanities and Social Sciences in Colleges and
Universities of Guangdong Province (Grant No. 2020WCXTD008); Natural Sciences Key Projects of Universities
in Guangdong Province (Grant No. 2019KZDXM042).

Abstract

Abstract: In this paper, the wave equation defined in a semi-infinite cylinder is considered,
in which the nonlinear damping and source terms is included. By setting an arbitrary
parameter greater than zero in the energy expression, the fast growth rate or decay rate
of the solution with spatial variables is obtained by using energy analysis method and
differential inequality technique. Secondly, we obtain the asymptotic behavior of the
solution on the external domain of the sphere. In addition, in this paper we also give
some useful remarks which show that our results can be extended to more models.

Key words: Wave equation, Energy analysis, Semi-infinite cylinder, Spatial asymptotic properties

CLC Number:

O175.29

LI Yuan-fei. Spatial Asymptotic Properties of a System Wave Equations with Nonlinear Damping and Source Terms[J]. Chinese Quarterly Journal of Mathematics, 2021, 36(1): 67-78.

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Spatial Asymptotic Properties of a System Wave Equations with Nonlinear Damping and Source Terms

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