关于抛物型方程的混合边值问题

On Mixed Boundary Value Problems for Parabolic Equations

本文讨论了二阶线性抛物型方程在圆柱体区域上的一类混合边值问题,这种边值问题包含Dirichlet问题,一些Neuman问题和第三边值问题作为特殊情形.文中使用了切片法和参考文献[1]中的一些结果,证明了在通常条件下以上边值问题解的存在性与唯一性.投有看到其他人解决过本文中所提的问题.此外,对于较一般二阶拟线性抛物型方程的相应边值问题,也可使用类似于本文中的方法去解决.

In this paper, we discussed a kind of mixed boundary value Problems for linear parabolic e-quations in a cylinder domain, Which include the Dirichlet Problem, some Neumann problem and third boundary value problem as their special cases, By using the method of cut-piece and the results of elliptic boundary value problems in [1]. we proved that the above mixed problems have a unique solutions.