含有梯度和非局部源的快速扩散方程解的熄灭  

Extinction for the Fast Diffusion Equation with Gradient and Nonlocal Source

作　　者：张海星[1] 陈玉娟[1] 顾紫怡 

机构地区：[1]南通大学理学院,江苏南通226019

出　　处：《南通大学学报（自然科学版）》2016年第1期66-70,共5页Journal of Nantong University(Natural Science Edition)　

基　　金：国家自然科学基金项目(11271209);南通大学研究生科技创新计划项目(YKC14041);南通大学大学生实践创新项目(2015008)

摘　　要：研究了含有梯度项和非局部源的快速扩散方程u_t=Δu^m+λ︱Δu︱~q+a∫_Ωu^pdx的弱解在有限时间内熄灭的问题,其中ΩR^N(N>2),0<m<1,q,a,λ,p>0.如果(i)m<p<1+m,m<q≤2/3-m,且初值充分小,或者(ii)m=q<p<1+m,q≤2/3-m,对任意初值u0,当λ,a充分小时,弱解u(x,t)在有限时间熄灭.In this study the phenomenon for the extinction of solutions infinite time of the fast diffusion equation with gradient and nonlocal source ut= Δu^m＋ λ︱ u︱^q＋ a∫Ωu^pdx was studied, in a bounded domain ΩR-Nwith N 〉2,0 〈m 〈1, q, a, λ, p 〉0. It was shown that if（i）m 〈p〈 1 ＋ m, m 〈q ≤2/3-m, and with sufficiently small initial data, or（ii）m = q p 1 ＋ m, q≤2/3-m, for any initial data u0, when λ, a were sufficiently small, the weak solution u（x, t） vanished infinite time.

关 键 词：快速扩散方程 非局部源 梯度项 熄灭 

分 类 号：O175.29[理学—数学]