一类具有非线性项的弱耦合半线性双波动系统全局解的非存在性

Nonexistence of Global Solutions to a Class of Weakly Coupled Semilinear Double-Wave System with Nonlinear Terms

考虑了一类非线性项的弱耦合半线性双波动系统在次临界情况下解的爆破问题:首先,引入若干时变泛函,结合微分不等式方法,得到了该泛函的迭代框架和第一下界;然后,运用迭代技巧和切片方法,证明了该双波动系统柯西问题解的爆破,并推出了其解的生命跨度上界。

Blow-up of solutions to a class of weakly coupled semilinear double-wave system with nonlinear terms in the subcritical case is considered.By introducing some time-dependent functional associated with differential inequality methods,an iteration frame and the first lower bound of solutions are obtained.Then,blow-up of solutions to the Cauchy problem is proved via the iteration technique and slicing methods.Meanwhile,the upper bound of the lifespan for solutions is derived.