On Neumann boundary problem for strongly degenerate parabolic-hyperbolic   equations on a bounded rectangle
  We study a Neumann type initial-boundary value problem for strongly degenerate parabolic-hyperbolic equations under the nonlinearity-diffusivity condition. We suggest a notion of entropy solution for this problem and prove its uniqueness. The existence of entropy solutions is also discussed. 
Yuxi Hu and Yachun Li
math.AP