一类非线性Klein-Gordon方程组初边值问题的整体经典解

Global Classical Solution for A Nonlinear Klein Gordon System

讨论了 Klein- Gordon方程组utt-Δu +α2 u +a2 uv2 =f (x,t) ,vtt-Δ v +β2 v +b2 u2 v =g(x,t)初边值问题的经典解 ,这里 f (x,t) ,g(x,t)为实值函数 ,α,β,a,b都为常数 .应用 Galerkin方法得到了上述耦合方程组在 Rn(1≤ n≤ 3)

This paper discusses the initial boundary value problem for the following Klein Gordon systemu tt -Δu+α 2u+a 2uv 2=f(x,t), v tt -Δv+β 2v+b 2u 2v=g(x,t)where f(x,t),g(x,t) are given real functions, α,β,a,b are constants. By employing the well known Galerkin method, we prove that this problem has an unique global classical solution in any smooth bounded domain ΩR n, 1≤n≤3.