方程u_t＝u_（xxt）＋σ（u_x）_x含第二类边界条件的初边值问题（Ⅱ）─

Initial-Boundary Value Problems of Equation u_t = u_(xxt)+ σ(u_x)_x Including Second Boundary Conditions (Ⅱ)-Smoothness, Asymptotic Behavior and Blow-up

本文在文［１］基础上进一步研究Ｓｏｂｏｌｅｖ－Ｇａｌｐｅｒｎ型方程ｕｔ＝ｕｘｘｔ＋σ（ｕｘ）ｘ具边界条件ｕｘ（０，ｔ）＝ｕｘ（１，ｔ）＝０与ｕ（０，ｔ）＝ｕｘ（１，ｔ）＝０的初边值问题。设σ（Ｓ）与初始函数满足适当的光滑性条件且σ（ｚｉ）（０）＝０（ｉ＝１，２，…，某个ｎ），得到强解相应的光滑性；并讨论了解的渐适性与ｂｌｏｗ－ｕｐ．

This paper based on [1] further studies the initial-boundary value problems of equation of Sobolev-Galpern type ut= uxxt+ σ(ut)x with boundary conditions ux(0, t) =ux(1, t) = 0 and u(0, t) = ux(1, t) = 0. Suppose that σ(s) and the initial function satisfy certain smoothness condi-tions and σ(zi)(0) = 0(i = 1, 2, …, acertain n), obtain corresponding smoothness of the strong solution; finally the asymptotic behavior andblow-up of solution are discussea.