I'm trying to solve the mentioned coupled PDEs with Matlab toolbox. I don't know how to specify the coefficients for the coupled mixed terms. Any help will be highly appreciated.
You can use assempde with c as a 2x2x2x2 tensor in the 2D case according to the docs. There is also a thread here that might be helpful: http://www.mathworks.com/matlabcentral/newsreader/view_thread/311746