| 一类a+b型浅水波方程的爆破现象和无限传播速度研究 |
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| 引用本文： | 赵永叶. 一类a+b型浅水波方程的爆破现象和无限传播速度研究[J]. 广州航海高等专科学校学报, 2020, 28(1): 66-69. DOI: 10.3969/j.issn.1009-8526.2020.01.014 |
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| 作者姓名： | 赵永叶 |
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| 作者单位： | 广州航海学院 基础教学部,广东 广州510725 |
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| 基金项目： | 广州航海学院创强项目青年创新人才类项目 |
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| 摘 要： | 本文研究了一类包含了Camassa-Holm(CH)和Degasperis-Procesi(DP)方程的非线性浅水波方程.首先建立了这类方程在Sobolev空间中解的局部适定性,爆破性.其次,我们讨论了这类方程的无限传播速度:如果初始值u0(·)具有紧支集,那么方程以u0(·)为初值的局部解u(t,·)不再具有紧支集,并且它在存在区间内呈现指数衰减的性质.
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| 关 键 词： | 浅水波方程 爆破性 无限传播速度 |
The Blow Up Phenomenon and Propagation Speed for a Class of Shallow Wter Equation |
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| ZHAO Yong-ye. The Blow Up Phenomenon and Propagation Speed for a Class of Shallow Wter Equation[J]. Journal of Guangzhou Maritime College, 2020, 28(1): 66-69. DOI: 10.3969/j.issn.1009-8526.2020.01.014 |
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| Authors: | ZHAO Yong-ye |
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| Affiliation: | (Department of Bosic Courses,Guangzhou Maritime University,Guangzhou Guangdong 510725,China) |
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| Abstract: | In this paper we study a kind of equation which includes the famous Cammassa-Holm(CH)and Degasperis-Procesi(DP)equation as special cases.We firstly study the local wellposedness in Sobolev space and the blow-up for the system.Secondly,infinite propagation speed for the system is proved in the following sense:while the corresponding nontrivial solution with compactly supported initial datum does not have compact-support any longer in its lifespan,it will decay exponentially at infinity throughout its evolution. |
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| Keywords: | shallow water equation blow up infinite propagation speed |
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