一类非线性Klein-Gordon方程组的初边值问题

Initial Boundary Value Problems for System of Nonlinear Klein-Gordon Equations

本文旨在讨论下述Kiein-Gordon方程组的初边值问题.这里f(x,t),w(x,t)为实值函数,α,β为质量常数,g,h为相互作用常数.本文应用Galerkin方法得到上述耦合方程在R^n(1≤n≤3)中任一具光滑边界的有界域中的初边值问题解的整体存在性和唯一性.

This paper is devoted to considering the following system of nonlinetr Klein-Gordon equationsu_u-△u+α~2u+g^2v^2u=f(x,t) v_u-△v+β~2v+h^2U^2v=ω(x,t) for Its initial boundary valoe problem. By employing the well-known Galerkin's method,we establish the existence and uniqueness resuhs of the weak solution to the problem mentioned above in any smooth boundedt domain Ω≤R^p,1≤n≤3