| 关于一类具阻尼项的非线性波方程的Cauchy问题 |
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| 引用本文： | SONG Chang-ming,KONG De-xing (Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China, Department of Mathematics and Physics,Zhongyuan Institute of Technology,Zhengzhou 450007,China). 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 |
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| 作者姓名： | SONG Chang-ming KONG De-xing (Department of Mathematics Shanghai Jiaotong University Shanghai 200240 China Department of Mathematics and Physics Zhongyuan Institute of Technology Zhengzhou 450007 China) |
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| 作者单位： | [1]DepartmentofMathematics,ShanghaiJiaotongUniversity,Shanghai200240,China／／DepartmentofMathematicsandPhysics,ZhongyuanInstituteofTechnology,Zhengzhou450007,China [2]DepartmentofMathematics,ShanghaiJiaotongUniversity,Shanghai200240,China |
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| 基金项目： | Supported by the National Natural Science Foundation of China(10371073) |
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| 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.
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| 关 键 词： | 非线性波函数 柯西问题 全局解 凹性法 偏微分方程 |
On the Cauchy Problem for a Class of Nonlinear Wave Equations with Damping Term |
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| SONGChang-ming KONGDe-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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| Authors: | SONGChang-ming KONGDe-xing |
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| 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 abovementioned 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. |
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| Keywords: | nonlinear wave equation Cauchy problem global solution concavity method |
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