论文标题
关于具有非重新边界条件的抛物线差分运算符的初始边界价值问题
On initial boundary value problem for parabolic differential operator with non-coercive boundary conditions
论文作者
论文摘要
我们考虑在$ {\ Mathbb r}^n $中，具有非重新边界条件的二阶统一的均匀的2-副差分差分运算符的初始边界值问题。在这种情况下，与强制性情况相比，Sobolev类型空间中解决方案的平滑度丧失。通过Faedo-Galerkin方法，我们证明问题在特殊的Bochner空间中具有独特的解决方案。
We consider initial boundary value problem for uniformly 2-parabolic differential operator of second order in cylinder domain in ${\mathbb R}^n $ with non-coercive boundary conditions. In this case there is a loss of smoothness of the solution in Sobolev type spaces compared with the coercive situation. Using by Faedo-Galerkin method we prove that problem has unique solution in special Bochner space.
