一类带阻尼项和记忆项的波动方程解的破裂
Blow-up of Solution to a Wave Equation with Damping Term and Memory Terms
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摘要: 在外区域上研究了一类带散射阻尼项和组合记忆项的波动方程的初边值问题。 当非线性项指数
p 与q 满足一定条件时,利用检验函数方法和迭代方法,在不同维数情形证明了问题的解会在有限时间破裂,并且建立了多项式形式的解的生命跨度的上界估计。Abstract: This paper is devoted to studying the initial boundary value problem for a wave equation with scattering damping term and combined memory terms on exterior domain. Blow-up of solution in finite time to the problem in different dimensions are proved under certain assumptions for the exponents p and q in nonlinear terms. In addition, upper bound lifespan estimates of solution in polynomial form are established by taking advantage of test function technique and iteration method.