【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.更多还原

【Abstract】 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,p>1,α>0,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.更多还原