非线性Klein-Gordon方程解的Blow-up

Blow-Up of Solutions of Nonlinear Klein-Gordon Equations

本文讨论非线性Klein-Gordon 方程的混合问题{u(■)—△u+u=F(u,Du,D_xDu) (t,x)∈(0,T)×Ωu(0,x)=h(x) u_t(0,x)=g(x),x∈Ω■u/■v=0■在F(u,Du,D_xDu)≥p sum from i=1 to n u_(X_i)~2+qu_t^2+u 这里(p>0,q>0) 及■_■■^(ph)(x)×g(x)dx>0时,得到该问题的解在有限时间内爆破.

This paper discusses the mixed problems of nonl■near Klein-Gordon equations ■u■—△u+u=F(u,Du,D_xDu),(t,x)∈(0,T)×Ω. u(0,x)=h(x),u■(0,x)=g(x),x∈Ω, ■u■v■Ω=0. When F(u,Du,D_xDu)≥p■u■+qu_t^2+u,(where P>0,q>0)and■(x)g(x) dx>0,That the solutions of the problems blow up in a finite time is obtained.