非线性波动方程整体解的存在性与唯一性

Existence and uniqueness of global solution to cauchy problem of nonlinear wave equation

设R^n为n维空间,f(t,x,u)是R^+×R^(n+1)上的实连续函数。本文讨论 u_u-△u+λu_1+μu=f(t,x,u),λ,u>0 (1) u(0,x)=u_0(x),u_1(0,x)=u_1(x).x∈R^n (2)的整体解的存在性与唯一性。

The existence and uniqueness of global solution to the cauchy problem of nonlinear wave equation are proved: u_u-Δu+λu_t+μu=f(t,x,u)by using fixed point theorem and sobolev's embedding theorem.