When I try to numerically solve the following set of PDEs, I get the following error:
NDSolve::indexss: The DAE solver failed at t = 0.`. The solver is intended for index 1 DAE systems and structural analysis indicates that the DAE is structurally singular.
After careful examination of the equations by me and my colleagues, we don't understand why these equations are not numerically solvable. Please let me know if you see any hints of why.
The code is attached and included below as an image (the actual code didn't look good when pasted from Mathematica).