具有齐次Neumann边界条件的抛物p-Laplace方程解的爆破以及不熄灭问题  

Blow-up and Non-extinction of Solution to a Parabolic p-Laplace Equation with Homogeneous Neumann Boundary Conditions

作　　者：贺艺军[1] 周芬 王华[2] HE Yijun;ZHOU Fen;WANG Hua(School of Mathematical Sciences, Shanxi University, Tai yuan 030006, China;College of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China)

机构地区：[1]山西大学数学科学学院,山西太原030006 [2]太原科技大学应用科学学院,山西太原030024

出　　处：《山西大学学报（自然科学版）》2018年第2期251-255,共5页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11401351);山西省回国留学人员科研资助项目(2016-009);太原科技大学2015年博士科研启动基金(20152042)

摘　　要：研究了R^n中有界区域上如下p-Laplace抛物型方程u_t-div(|▽u|^(p-2)▽u)=|u|^(q-2)ulog|u|-1/|Ω|∫_Ω|u|^(q-2)ulog|u|dx在齐次Neumann边界条件下解的爆破以及不熄灭问题。对于1<p<2的情形,证明了在初始能量非正,q>2时解在有限时刻爆破,而1<q≤p时解在有限时间内不熄灭。We study the blow-up and non-extinction of solution to a parabolic p-Laplace equation ut-div（｜▽u｜p-2^▽u）=｜u｜^q-2ulog｜u｜-1/｜Ω｜∫Ω｜u｜^q-2ulog·u｜dx subject to homogeneous Neumann boundary value condition.For the case of 1p2,we prove that under the condition of non-positive initial energy,the solution blows up in finite time if q2,and the solution does not extinct in finite time if 1q≤p.

关 键 词：P-LAPLACE方程 NEUMANN边界条件 爆破 不熄灭 

分 类 号：O175.2[理学—数学]