Any update on this PDE?
Mathematica does not currently solve these type of problems, which we're very much aware of.
In Mathematica 10 we have introduced a wide range of new capabilities to DSolve and related functionality, these can be exposed by the "Show changes" button here: http://reference.wolfram.com/language/ref/DSolve.html
Providing analytical and numerical solutions to differential equations continues to be an important component of our research and development, this family of problems is of particular interest to us and will be the focus of future updates to the Wolfram Language and Mathematica functionality.
Thanks for your comment.
Yes, I have tried this particular system in MMA 10, but it still does not perform as expected.
I am in general very much like to explore more in MMA. But for my research purpose at the moment, I will have to stick with Maple, because it is the only Computer Algebraic package that gives me what I need. The PDEs actually form from a null space of particular matrices. So in practice, I demand much more than this "simple" and small example.
It would be nice to see more of this development in the future.