带有边界阻尼的一类非线性波动方程适定性问题

发布时间：2018-03-21 22:10

本文选题：带有边界阻尼　切入点：非线性　出处：《科技通报》2017年09期 　论文类型：期刊论文

【摘要】：近年来,人们对于非线性波动方程的适定性问题进行了广泛而又深入的研究,取得了一定程度的发展。目前,非线性波动方程的适定性问题研究采用的方法是对一类非线性波动方程的初边值问题解的性态进行研究,以Sobolev空间的性质为工具,利用反散射方法,研究该方程在线性的边界条件下解的适定性,为波动方程的振动问题提供了研究依据,但该方法存在过程较为复杂的问题。因此,提出带有边界阻尼的一类非线性波动方程适定性问题。首先,对带有边界阻尼的非线性波动方程进行正则解的求解,即先讨论非线性波动方程正则解存在性的必要和充分条件,总结出求取正则解的通式;其次,对方程进行Strichartz估计,得到正则解的具体解形式;最后以非线性波动方程正则解计算的结果完成对非线性波动方程正则解适定性的证明。
[Abstract]:In recent years, people have made extensive and in-depth research on the fitness problem of nonlinear wave equations, and have made some progress. The method used in the study of the fitness problem of nonlinear wave equation is to study the behavior of the solution of the initial boundary value problem of a class of nonlinear wave equation. The property of Sobolev space is used as a tool, and the backscattering method is used. The study of the fitness of the solution of the equation under the linear boundary condition provides a basis for the study of the oscillation problem of the wave equation, but the method has some problems in the process. In this paper, a class of nonlinear wave equations with boundary damping is proposed. Firstly, the regular solutions of nonlinear wave equations with boundary damping are solved, that is, the necessary and sufficient conditions for the existence of regular solutions of nonlinear wave equations are discussed. The general formula for finding regular solutions is summarized. Secondly, the concrete solution form of the regular solution is obtained by Strichartz estimation of the equation. Finally, the proof of the fitness of the regular solution of the nonlinear wave equation is completed by the result of the regular solution calculation of the nonlinear wave equation.
【作者单位】：河南财政金融学院信息工程系;
【基金】：基金项目河南省智慧城市建设方案与评价指标体系研究(2016BSH003)
【分类号】：O175.29

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