一个带非线性边界条件的强耦合抛物方程组的整体存在性与爆破(英文)  

Global Existence and Finite Time Blow-up for a Strongly Coupled Parabolic System with Nonlinear Boundary Conditions

作　　者：陈友朋[1] 谢春红[2] 

机构地区：[1]盐城师范学院数学系,江苏盐城224002 [2]南京大学数学系,南京210093

出　　处：《应用数学》2003年第3期23-30,共8页Mathematica Applicata

摘　　要：本文处理带非线性边界条件 u n=uα, v n=vβ ,(x ,t) ∈ Ω× (0 ,T)的抛物方程组ut =vpΔu ,vt=uqΔv ,(x ,t) ∈Ω× (0 ,T) ,其中Ω RN 为一个有界区域 ,p ,q>0和α ,β≥ 0为常数 .研究了上述问题正解的整体存在性和爆破 ,建立了整体存在和爆破的新标准 .证明了当max{p+β,q+α}≤ 1时正解 (u ,v)整体存在 ,当min{p+β ,q+α}>1且max{α ,β}<1时正解 (u ,v)This paper deals with the strongly coupled parabolic system u t=v p Δ u,v t=u q Δ v,(x,t)∈Ω×(0,T) subject to nonlinear bounded conditions un=u α,vn=v β,(x,t)∈Ω×(0,T),where ΩR N is a boundary domain,p,q>0 and α,β≥0 are constants.Global existence and finite time blow up of the positive solution of the above problem are studied.New criteria for global exitence and finite time blow up are established.It is proved that if max {p+β,q+α}≤1 then the positive solution (u,v) of the above problem exists globally,and if min {p+β,q+α}>1 and max {α,β}<1 then the positive solution (u,v) blows up in finite time.

关 键 词：非线性边界条件 强耦合抛物方程组 整体存在性 爆破 正解 上解 下解 

分 类 号：O175.26[理学—数学]