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  本文選題：高階Camassa-Holm方程 + 爆破��； 參考：《江蘇大學》2017年碩士論文

【摘要】：非線性偏微分方程解的爆破性質(zhì)包括解的爆破準則、爆破速率、爆破點集等,是非線性方程研究的基本問題之一。本文主要研究的是二階Camassa-Holm方程問題解的相關爆破性質(zhì)。首先通過一系列的先驗估計得到二階Camassa-Holm方程解的爆破準則和爆破速率,然后利用閉集的相關性質(zhì)得到爆破點集,最后得到了方程的初值解在滿足一定的條件下解的爆破點集和非爆破點集。全文主要內(nèi)容共分為三部分:第一部分研究了二階Camassa-Holm方程在初值條件有限的情況下解的爆破準則和爆破速率;第二部分利用閉集的相關性質(zhì)給出了二階Camassa-Holm方程的爆破點集;第三部分利用先驗估計給出了二階Camassa-Holm方程的初值條件在R上非負或是不變號的情況下的非爆破點集。
[Abstract]:The blasting properties of the solutions of nonlinear partial differential equations include the blasting criterion of solutions, the blasting rate, the set of blasting points, and so on. It is one of the basic problems in the study of nonlinear equations. In this paper, we mainly study the related blasting properties of the solutions of the second order Camassa-Holm equation problem. First, by a series of priori estimates, the blow-up criterion and blasting rate of the solution of the second order Camassa-Holm equation are obtained, and then the set of blasting points is obtained by using the properties of the closed set. Finally, the burst point set and the non-burst point set of the initial solution of the equation are obtained under certain conditions. The main contents of this paper are divided into three parts: in the first part, the blasting criterion and blasting rate of the solution of the second order Camassa-Holm equation are studied under the condition of limited initial value conditions, the second part gives the blasting point set of the second order Camassa-Holm equation by using the properties of the closed set. In the third part, by using the prior estimator, we give the set of non-burst points under the condition that the initial value condition of the second order Camassa-Holm equation is nonnegative or invariant on R.
【學位授予單位】：江蘇大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

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