一类带阻尼项和负质量项的波动方程解的破裂

Blow-up of solution to a wave equation with damping term and negative mass term

在外区域上研究一类带阻尼项、负质量项和组合非线性项的变系数波动方程的初边值问题.通过引入乘子,利用检验函数方法与迭代方法,在小初值时得到问题的解会在有限时间内破裂,进而给出其生命跨度的上界估计.

This paper is concerned with the initial boundary values problem of a variable coefficient wave equation with damping term,negative mass term and combined nonlinearities on exterior domain.Using the multiplier and applying test function technique together with iterative approach,it is deduced that a solution to the problem with small initial values will blow-up in finite time.Moreover,upper bound lifespan estimate of solution is established.