Hi,
pdepe is designed for PDEs where the diffusion term is relatively large compared with the convection term. In your equations the convection terms are much larger than the diffusion terms. A key parameter is the cell Peclet number which is c*h/(2*d) where c is the convection coefficient, d is the diffusion coefficient, and h is the size of each cell (element) in the mesh. For the algorithm to be stable this number should be less than one. You can find discussion of this in books on numerical methods for convection-diffusion equations. (e.g. page 508 in http://www.amazon.com/Computational-Science-Engineering-Gilbert-Strang/dp/0961408812).
Some approaches for solving this class of problem add some "artificial" diffusion-- i.e. a larger diffusion coefficient than actually exists. You might try this and see how that affects the solution. Also, you have a relatively coarse mesh with only 29 elements along the 2.8 unit length. In general, the mesh density affects accuracy and, in this case, also the stability of the method. I recommend experimenting with a single, simple convection diffusion equation to get a feel for how these parameters affect the solution.
Finally, I noticed one thing about your problem that seems odd. The length is 2.8 units, the velocity is on the order of 550, and you are solving the equations for a time span of 200. It seems like whatever is being convected will be transported well off the model long before you reach the final time?
Hope this helps.
Bill
