本文選題：雙成分Camassa-Holm方程 + 零階耗散��； 參考：《云南師范大學(xué)》2015年碩士論文

【摘要】：本文研究帶零階耗散項λu的雙成分Camassa-Holm方程的Cauchy問題.首先根據(jù)Kato定理建立解的局部適定性,然后研究了解的blow-up現(xiàn)象和整體存在性.最后,研究方程整體弱解的存在性.全文共五章.第一章,介紹了耗散型的雙成分Camassa-Holm方程的研究背景和本文的主要結(jié)果,及與本文相關(guān)的一些符號.第二章,證明方程Cauchy問題的解當(dāng)z0=u0-ρ0∈Hs×Hs-1,s≥2是局部適定.第三章,研究了方程Cauchy問題的解的爆破機制,并給出導(dǎo)致解發(fā)生爆破的兩個充分條件.第四章,研究了方程Cauchy問題的解的整體存在性.第五章,研究了方程Cauchy問題的整體弱解的存在性.
[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，

本文編號：2046514