带有吸附项的边界扩散退化抛物方程解的性质  

Properties of the Boundary Degenerate Parabolic Equation with Adsorption Item

作　　者：谢清梅[1] 詹华税[1] 

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2012年第1期71-74,共4页Journal of Jimei University：Natural Science

基　　金：福建省自然科学基金资助项目(2009J01009);集美大学潘金龙科研基金资助项目(C510071)

摘　　要：研究带有吸附项的边界扩散退化抛物方程u/t=div(dα︱▽u︱p-2▽u)-uq,(x,t)∈QT=Ω×(0,T),其中:ΩRN是一个边界适当光滑的有界区域;d(x)=dist(x,Ω).验证了当α≥p-1时,该方程存在只与初值条件有关的解,而且是唯一的;当0<α<p-1时,方程存在与初值条件及边界条件有关的唯一解.The boundary degenerate parabolic equation with adsorption item Эu/Эt=dix（d^a｜u｜^p-2u）-u^q,（x,t）∈Qr=Ω×（0,T） was studied, where OCRN was a bounded domain with appropriately smooth boundary OO,d（x） = dist（x, OO） , and it was proved that if a≥ p - 1 , the equation was admitted a unique solution subject only to a given initial datum without any boundary value condition. While if 0 〈 a 〈 p - 1 , for a given initial datum, the equation admitted different solutions for different boundary value conditions.

关 键 词：边界退化 扩散方程 存在性 唯一性 

分 类 号：O175.27[理学—数学]