一类非线性发展方程的第二边值问题

SECOND BOUNDARY PROBLEMS FOR A CLASS  OF NONLINEAR EVOLUTION EQUATIONS

研究具第二边界条件ｕｎ＝ｂ（ｕ）的非线性抛物方程ｕｔ＝（ａ（｜ｕ｜）ｕ）＋ｆ（ｕ）的整体解，使用上、下解方法，在关于ａ，ｂ与ｆ的适当假定下，得到了上述第二边值问题正解的整体存在及在有限时间ｂｌｏｗ－ｕｐ的条件。

This paper deals the global solutions of nonlinear parabolic equations ut=(a(|u|)u)+f(u) with second boundary conditions un=b(u) on Ω×(0,T). We using upperlower solution method,under appropriate assumptions on a,b and f obtained the condition of global existence and blow up in finite time of positive solution of this problem.