关于一类具阻尼项的非线性波方程的 Cauchy问题

数学季刊 ›› 2005, Vol. 20 ›› Issue (2): 111-120.

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关于一类具阻尼项的非线性波方程的 Cauchy问题

Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China; Department of Mathematics and Physics, Zhongyuan Institute of Technology, Zhengzhou 450007, China

收稿日期:2004-12-09 出版日期:2005-06-30 发布日期:2024-01-17
作者简介: SONG Chang-ming(1965-),male,native of Zhengzhou,Henan,an associate professor of Zhongyuan Institute of Technology,Ph.D.,engages in partial differential equations.
基金资助:
Supported by the National Natural Science Foundation of China(10371073)；

On the Cauchy Problem for a Class of Nonlinear Wave Equations with Damping Term

Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China; Department of Mathematics and Physics, Zhongyuan Institute of Technology, Zhengzhou 450007, China

Received:2004-12-09 Online:2005-06-30 Published:2024-01-17
About author: SONG Chang-ming(1965-),male,native of Zhengzhou,Henan,an associate professor of Zhongyuan Institute of Technology,Ph.D.,engages in partial differential equations.
Supported by:
Supported by the National Natural Science Foundation of China(10371073)；

摘要/Abstract

摘要： The paper concerns with the existence, uniqueness and nonexistence of global solution to the Cauchy problem for a class of nonlinear wave equations with damping term. It proves that under suitable assumptions on nonlinear the function and initial data the above-mentioned problem admits a unique global solution by Fourier transform method. The sufficient conditions of nonexistence of the global solution to the above-mentioned problem are given by the concavity method.

关键词: , nonlinear wave equation, Cauchy problem, global solution, concavity method

Abstract: The paper concerns with the existence, uniqueness and nonexistence of global solution to the Cauchy problem for a class of nonlinear wave equations with damping term. It proves that under suitable assumptions on nonlinear the function and initial data the above-mentioned problem admits a unique global solution by Fourier transform method. The sufficient conditions of nonexistence of the global solution to the above-mentioned problem are given by the concavity method.

Key words: , nonlinear wave equation, Cauchy problem, global solution, concavity method

中图分类号:

O175.29

宋长明, 孔德兴. 关于一类具阻尼项的非线性波方程的 Cauchy问题[J]. 数学季刊, 2005, 20(2): 111-120.

SONG Chang-ming, KONG De-xing. On the Cauchy Problem for a Class of Nonlinear Wave Equations with Damping Term[J]. Chinese Quarterly Journal of Mathematics, 2005, 20(2): 111-120.

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关于一类具阻尼项的非线性波方程的 Cauchy问题

On the Cauchy Problem for a Class of Nonlinear Wave Equations with Damping Term

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