一类非线性双曲方程解的存在唯一性

Existence and Uniqueness of Solution for Nonlinear Hyperbolic Equation

运用Galerkin法研究了一类非线性双曲方程初边值问题解的存在唯一性.考虑到发展方程和无穷维动力系统的紧密联系,首先定义了一个算子半群,运用索伯列夫空间中的嵌入定理结合半群对非线性项进行恰当估计,减少了估计中的运算量,得到所研究问题解的存在唯一性.

In this paper,the solution to the initial boundary value problem for nonlinear hyperbolic equation is investigated with the method of Galerkin.In view of the close relationship between evolution equations and infinite-dimensional dynamical systems,an operator semigroup is defined.Using this semigrop and the embedding theorem of Sobolev space,the nonlinear term is estimated and the computational complexity is reduced.The existence and uniqueness of solution for this class of equation are obtained.