边界退化的奇异扩散方程解的正则性  

The Regular Properties of the Singular Diffusion Equation with Boundary Degeneracy

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）》2011年第5期389-391,共3页Journal of Jimei University：Natural Science

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

摘　　要：研究在边界退化的奇异扩散方程u/t=div(dα︱▽u︱p-2▽u),(x,t)∈QT=Ω×(0,T),其中ΩRN是一个边界适当光滑的有界区域,p>1,α>0,d(x)=dist(x,Ω).在假设解的唯一性成立的前提下,证明了这种热传导问题的弱解具有与一般热传导问题的弱解相似的正则性.The singular diffusion equation with boundary degeneracy u/t=div（dα︱▽u︱p-2▽u）,（x,t）∈QT=Ω×（0,T） was studied,where ΩRN was bounded domain with appropriately smooth boundary,p1,α0,α≠1,and d（x）=dist（x,Ω）.Under the assumption on the uniqueness of the weak solution,the regular properties of the weak solution similar to those of the weak solution for a general heat conduction without degeneracy on the boundary were obtained.

关 键 词：边界退化 扩散方程 唯一性 正则性 

分 类 号：O175.27[理学—数学]