一类含加权非线性项的Moore-Gibson-Thompson方程初边值问题解的破裂

Blow-up of solution for the initial boundary value problem of Moore-Gibson-Thompson equation with weighted nonlinear term

本文在3维空间外区域(即3维空间中有界区域的补集)中研究了一类包含加权非线性项的Moore-Gibson-Thompson方程初边值问题的解的破裂,其中的边界条件分别为Dirichlet边界条件和Neumann边界条件.本文构造了检验函数,运用迭代方法在次临界和小初值情形下证明问题的解将在有限时间内破裂,并给出了解的生命跨度的上界估计.

In this paper,the blow-up of solution for the initial boundary value problem of Moore-Gibson-Thompson equation with weighted nonlinear term on exterior domain in 3D space,i.e.,the complement of some bounded regions in 3D space,is established,where the boundary conditions are Dirichlet boundary and Neumann boundary conditions,respectively.By using the test function technique and taking advantage of it⁃eration method,the blow-up of solution with small initial values in the sub-critical case is established.Addi⁃tionally,the upper bound lifespan estimate of solution is obtained.