一类带非局部源项的p-Laplace方程解的整体存在与爆破  

Existence of Global Solutions and Blow-up for a p-Laplacian Parabolic Equations

作　　者：李建军[1] 吕雅婷 LI Jianjun;LV Yating(College of Science,Liaoning Technical University,Fuxin 123000,China)

机构地区：[1]辽宁工程技术大学理学院,辽宁阜新123000

出　　处：《应用数学》2021年第2期397-407,共11页Mathematica Applicata

摘　　要：本文研究一类在Neumann边值条件下带局部源项的p-Laplace方程解的整体存在和爆破性.利用微分不等式技巧,通过构造辅助函数的方法,获得了方程的解整体存在和解在有限时间爆破的充分条件,以及爆破时间的上下界估计,推广了相关文献结论.The global existence and finte time blow-up for the classical solutions of a nonlinear reaction diffusion equation with p-Laplacian and nonlocal terms under Neumann boundary condition in a bounded domain are considered.By constructing auxiliary functions and using differential inequality techniques,we give the sufficient conditions for global existence versus finite time blow-up.In addition,we obtain upper bounds and lower bounds of the blow-up time.

关 键 词：整体存在 爆破 微分不等式 

分 类 号：O175.29[理学—数学]