一类具有导数型非线性项的弱耦合半线性双波动系统解的爆破

Blow-up of solutions to a class of weakly coupled semilinear double-wave systems with nonlinear terms of derivative type

考虑了一类具有导数型非线性项的弱耦合半线性双波动系统解的爆破现象.通过选择合适的泛函以及运用迭代方法,对p≠q时的弱耦合现象进行了深入研究,当p=q时退化为单个导数型半线性双波动方程,证明了非临界情况下其柯西问题解的全局非存在性.同时,导出了其解的生命跨度上界估计.

In this paper,blow-up of solutions to a class of weakly coupled semilinear double-wave systems with nonlinear terms of derivative type is considered.By choosing suitable functionals and using an p̸=qiteration technique,the weakly coupled phenomena are studied in-depth for the case when.For the p=qcase when,the solution is degenerated to a single semilinear double-wave equation with a nonlinear term of derivative type.Furthermore,the nonexistence of global solutions to the Cauchy problem in the subcritical case is proven.Meanwhile,the upper bound estimate of the lifespan of solutions is also derived.