二元混合物中的热传导方程解的爆破现象

The Blow-Up Phenomenon of Solutions of Heat Conduction Equation In Binary Mixtures

考虑了定义有界凸区域上二元固体混合物中的热传导方程,其中在区域的边界上满足局部非线性条件.通过对非线性条件以及初始值做适当限制,利用能量估计的方法,得到了爆破发生时爆破时间的下界.并且找到了解在有限时刻一定发生爆破的条件,得到了爆破时间的上界.

The heat conduction equation in a binary solid mixture on a bounded convex domain is considered,in which the local nonlinear conditions are satisfied on the boundary of the domain.By properly limiting the nonlinear conditions and the initial value,the lower bound of the blow-up time is obtained by using the method of energy estimation.The conditions that the blow up must occur at a finite time are found and the upper bound of blow-up time is obtained.