Qualitative behaviour for one-dimensional strongly degenerate parabolic problems
Corrado Mascia, Alessio Porretta, Andrea Terracina · Interfaces and Free Boundaries Mathematical Analysis Computation and Applications · 2006
We consider strongly degenerate convection-diffusion equations which mix possible parabolic and hyperbolic behaviour. We prove some qualitative properties of the solutions, in the one-dimensional case. In particular we study the evolution in time of the number of connected components of parabolic and hyperbolic regions and the continuity of the interfaces between the two phases.