一维非线性抛物型方程blow－up

Blow-up in one-dimensional nonlinear parabolic equation

考虑一维非线性抛物型方程ｕｔ＝（ｕｍ）ｘｘ＋ｕｐ在周期边界条件或Ｎｅｕｍａｎｎ边界条件下的初边值问题．证明ｂｌｏｗｕｐ集是有限和极限ｌｉｍｕ（ｘ，ｔ）＝ρ（ｘ）存在，ρ除了至多有限个奇点外是光滑函数．

n this paper,the author considers the initial boundary value problem for the nonlinear parabolic equation ui=(um)xx+up under the Neumann or the periodic boundary conditions.It is proved that the blow-up set is a finite set and that lim u(x,t) =ρexists,with ρ being a smooth function having at most finitely many singular points.