摘要
为了方便对一些典型的双曲型数学物理方程解的研究,本文着力于一类非线性双曲型方程弱解的存在唯一性的研究,且这类方程的双曲型算子是一般形式的双曲型算子。在非线性项f(u)满足Lipschitz条件的假设条件下,利用伽罗金逼近法和压缩映像原理等方法获得了这类方程初边值问题弱解的存在唯一性,另外,本研究提供了一类非线性双曲型方程弱解存在性及唯一性的一种证明方法。
In order to conveniently study some typical hyperbolic mathematical physics equations,this paper researches into the existence and uniqueness of weak solutions to a class of nonlinear hyperbolic equations,of which the hyperbolic operators are general hyperbolic operators.By making use of Galerkin-approximation,Contraction Theorem and so on,existence and uniqueness of weak solutions in the initial/boundary-value problem to the class hyperbolic equations are obtained.The study offers a method of proof of existence and uniqueness of weak solutions to a class of nonlinear hyperbolic equations.
出处
《石河子大学学报（自然科学版）》
CAS
2013年第1期122-126,共5页
Journal of Shihezi University(Natural Science)
基金
国家自然科学基金项目(10861014)
国家自然科学基金项目(11161057)
关键词
非线性双曲型方程
压缩映像
伽罗金逼近
弱收敛
nonlinear hyperbolic equations
Contraction Theorem
Galerkin-approximation
weak convergence
