一类带时间加权非线性项的波动方程解的破裂

Blow-up of Solution to the Wave Equation with Time Weighted Nonlinear Term

通过引入适当的乘子克服散射阻尼项的影响,构造检验函数并且利用迭代方法,得到n维空间中一类带散射阻尼项与时间加权非线性项的波动方程的小初值问题解的破裂,并给出其生命跨度的上界估计.

By introducing an appropriate multiplier to overcome the influence of scattering damping term,constructing a test function and making use of iterative approach,blow-up results of the solution to a small initial value problem of wave equation with scattering damping term and time weighted nonlinear terms in n space dimensions are obtained.In addition,the upper bound lifespan estimates of solution are presented.