修正Kawahara方程的收敛问题与色散爆破

摘要/Abstract

摘要： 该文主要研究修正Kawahara方程的收敛问题与色散爆破. 首先，利用傅里叶限制范数法，高低频分解技巧以及Strichartz估计, 该文用三种不同的方法证明在空间H^{s}(\mathbb{R})(s\geq\frac{1}{4})中，对几乎处处的x\in\mathbb{R}，当t\longrightarrow0时，u(x,t)\longrightarrow u_0(x)，其中u(x,t)是修正Kawahara方程的解，u_0(x)是其柯西问题的初值. 其次，利用Strichartz估计和傅里叶限制范数法该文证明在空间H^{s}(\mathbb{R})(s>0) 中，当t\longrightarrow0时，u(x,t)\longrightarrow U(t)u_0(x)(与x无关). 最后，该文给出方程解的色散爆破.

关键词: 修正Kawahara方程, 逐点收敛, 一致收敛, 色散爆破

Abstract: This paper is concerned with the convergence problem and dispersive blow-up of the modified Kawahara equation. Firstly, by using the Fourier restriction norm method，high-low frequency tecnique and Strichartz estimates， this paper uses three different methods to prove that for almost everwhere x \in R, when t\longrightarrow0，　 u(x,t) converges to u_0(x) in H^{s}(\mathbb{R})(s\geq\frac{1}{4})， where u(x,t) is the solution and u_{0}(x) is the data. Secondly, by using Strichartz estimates and Fourier restriction norm method, this paper prove that when t\longrightarrow0, u(x,t) converges to U(t)u_0(x) uniformly with respect to $x$. Finally, this paper presents the dispersive blow-up.

Key words: Modified Kawahara equation, Pointwise convergence, Uniform convergence, Dispersive blow-up

中图分类号:

王伟敏闫威. 修正Kawahara方程的收敛问题与色散爆破[J]. 数学物理学报, , (): 0-0.

Wei-Min WANG Wei Yan. The convergence problem and dispersive blow-up of the modified Kawahara equation[J]. Acta mathematica scientia,Series A, , (): 0-0.

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