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

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)在有限时刻爆破

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

This paper deals with the strongly coupled parabolic system ut = vp △u,vt = uq △v, (x,t)∈Ω×(0,T) subject to nonlinear bounded conditions u/ n=uα, v/ n=vβ,(x,t) ∈Ω×(0,T), whereΩ RN is a boundary domain, p,q ＞ 0 and α,β≥ 0 are constants. Global existence and finite timeblow-up of the positive solution of the above problem are studied. New criteria for global exitenceand finite time blow-up are established. It is proved that if max{ p+β, q+α}≤1then the positive so-lution (u,v) of the above problem exists globally,and if min{p+β, q+α}＞1 and max{α,β}＜ 1 thenthe positive solution (u,v) blows up in finite time.