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摘要
This article concerns the Cauchy problem for the damped nonlinear hyperbolic system Eutt+()u+ut=vp,t>0,xRN,u>0,v>0,Evtt+()v+vt=uq,t>0,xRN,u>0,v>0,u(x,0)=u0(x),ut(x,0)=u1(x),xRN,v(x,0)=v0(x),vt(x,0)=v1(x),xRN, where E>0 is a small parameter, 0<1,0<1,p,q1 satisfying pq>1 , and N1 is an integer.It is proved that if N/2<max((p+1)/(pq1),(q+1)/(pq1)), then every weak solution does not exist globally whenever the initial data satisfy RN{u0(x)+u1(x)}dx>0 or RN(v0(x)+v1(x))dx>0.
- 出版日期2013-4
