一类非线性耦合波动方程组解的整体不存在性

Global Nonexistence of Solutions for Nonlinear Coupled Wave Equations

研究了一类带有源项和线性阻尼的非线性耦合波动方程组的初边值问题,该系统可以描述受到外力作用和粘性阻尼以及摩擦阻尼作用的非线性系统的振动.通过构造合适的泛函和微分方程不等式,对外力源项、松弛函数以及非线性项的增长阶数加以一些约束条件,给出了当源项起主要作用时,具有负初始能量的耦合波动方程组的系统解不是整体存在的结论.

A nonlinear coupled viscoelastic wave equations system with source and damping terms was studied.This system can describe a nonlinear vibration system which was subjected to external force,viscous damping and friction damping.It is proved that the solution of the system is nonexistence when the source term plays a major role by constructing an appropriate functional and differential inequalities,and making constraints on source terms,relaxation function and nonlinear growth order number.