带有边界阻尼的一类非线性波动方程适定性问题  

Well Posed Problems for A Class of Nonlinear Wave Equations with Boundary Damping

作　　者：高瑞华 Gao Ruihua(Department of Information Engineering,Henan College of Finance and Taxation,Zhengzhou 451464,China)

机构地区：[1]河南财政金融学院信息工程系,河南郑州451464

出　　处：《科技通报》2017年第9期25-28,共4页Bulletin of Science and Technology

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)

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。In recent years,the problem of well posedness of nonlinear wave equations has been studiedextensively and deeply,and has achieved a certain degree of development.At present,the study ofoptimal problem of nonlinear wave equation with qualitative method is the initial boundary of a class ofnonlinear wave equations of state value solutions were studied in the Sobolev space as a tool,using theinverse scattering method,study the well posedness in the linear boundary conditions of the solution ofthis equation,provided the research basis for vibration the problem for the wave equation,but thismethod has a complex process problem.Therefore,a class of nonlinear wave equation with boundarydamping is considered.First of all,solving the regularized solution of nonlinear wave equation withboundary damping,first discusses the existence of the necessary regular solution of nonlinear waveequation and sufficient conditions,summed up the formula to calculate the regularized solution;secondly,to estimate Strichartz equation,get regular solution specific solutions;finally to nonlinear waveequation of regular solution the calculation results of the nonlinear wave equation of regular solutionprove well posedness.

关 键 词：带有边界阻尼 非线性 波动方程 正则解 适定性 

分 类 号：O175[理学—数学]