Blow-up solutions of some nonlinear hyperbolic systems
The paper deals with initial value problems for two types of systems of two semilinear wave equations \(u_{tt}=\Delta u+|v|^p, v_{tt}=\Delta v+|u|^q,\) and \(u_{tt}=\Delta u+|v_t|^p, v_{tt}=\Delta v+|u_t|^q (t>0, x\in \mathbb{R}^n)\) with compactly supported initial data. The author gives the bound \(B(n,p)\) such, that if \(1<pq<B(n,p),\) all nontrivial solutions of the above problems blow up in finite time.
scientific article; zbMATH DE number 1439636
scientific article