具强阻尼项的四阶弱耦合双曲方程组解爆破时间的下界估计

Estimate of Lower Bound for Blow-up Time of Solutions to Fourth-Order Weakly Coupled Hyperbolic Systems with Strong Damping Terms

考虑一类四阶非线性耦合双曲方程组解的生命跨度下界估计,通过构造合适的控制函数,利用能量估计法和Sobolev嵌入定理,给出控制函数满足的一阶微分不等式,并通过分析微分不等式的性质,给出所研究问题解的生命跨度下界估计.

We considered the lower bound for the lifespan of the solutions to a class of fourth-order nonlinear coupled hyperbolic systems.By constructing the appropriate control function,using the energy estimate method and Sobolev embedding theorem,we gave the first-order differential inequality satisfied by the control function,and gave the estimate of the lower bound for the lifespan of the solution of the problem by analyzing the properties of differential inequalities.