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Sep 28, 2011 at 1:41 comment added Nilima Nigam I'd have to agree- the problem, as stated, may not admit well-defined solutions. Set $c=0, d=1,a=-1,b=0$, and one finds Burger's equations. I can think of boundary data on the edges of the square which would lead to a lack of well-posedness. A numerical attack via finite differences would be reasonable to try.
Sep 27, 2011 at 19:38 history answered Paul Tupper CC BY-SA 3.0