具零阶耗散的双成分Camassa-Holm方程的解的研究

发布时间：2018-06-21 01:17

  本文选题：双成分Camassa-Holm方程 + 零阶耗散　； 参考：《云南师范大学》2015年硕士论文

【摘要】：本文研究带零阶耗散项λu的双成分Camassa-Holm方程的Cauchy问题.首先根据Kato定理建立解的局部适定性,然后研究了解的blow-up现象和整体存在性.最后,研究方程整体弱解的存在性.全文共五章.第一章,介绍了耗散型的双成分Camassa-Holm方程的研究背景和本文的主要结果,及与本文相关的一些符号.第二章,证明方程Cauchy问题的解当z0=u0-ρ0∈Hs×Hs-1,s≥2是局部适定.第三章,研究了方程Cauchy问题的解的爆破机制,并给出导致解发生爆破的两个充分条件.第四章,研究了方程Cauchy问题的解的整体存在性.第五章,研究了方程Cauchy问题的整体弱解的存在性.
[Abstract]:In this paper, the Cauchy problem of bicomponent Camassa-Holm equation with zero order dissipative term 位 u is studied. Firstly, the local fitness of solutions is established according to Kato theorem, and then the blow-up phenomenon and the global existence of the solution are studied. Finally, the existence of the global weak solution of the equation is studied. The full text consists of five chapters. In the first chapter, we introduce the research background of dissipative bicomponent Camassa-Holm equation, the main results of this paper, and some symbols related to this paper. In the second chapter, it is proved that the solution of the Cauchy problem for the equation is locally appropriate if z 0 u 0-蟻 0 鈭，

本文编号：2046514