一类带阻尼项和记忆项的波动方程解的爆破

Blow-up of Solution to a Wave Equation with Damping Term and Memory Term

研究一类带尺度不变阻尼项和记忆项的波动方程的小初值问题.当非线性项指数p与q满足一定条件时,通过构造泛函,利用检验函数方法和迭代方法,证明方程的解会在有限时间爆破,并给出解的生命跨度的上界估计.

The purpose of this paper is to study the initial value problem of a wave equation with scale-invariant damping term and combined memory term.Finite time blow-up of solution is proved by constructing functional and using the test function method together with the iteration method under certain assumptions for the exponents p and q in nonlinear terms.Meanwhile,the estimate for the upper bound lifespan of the solution is given.