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

作　　者：明森 范雄梅 MING Sen;FAN Xiong-Mei(School of Mathematics,North University of China,Taiyuan 030051,China;School of Data Science and Technology,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,太原030051 [2]中北大学大数据学院,太原030051

出　　处：《四川大学学报（自然科学版）》2024年第6期31-36,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：山西省基础研究计划资助项目(20210302123045,202103021223182)。

摘　　要：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.

关 键 词：加权非线性项 Moore-Gibson-Thompson方程初边值问题 破裂 生命跨度 

分 类 号：O175.29[理学—数学]