We study a convective problem of "mixed type" (i.e., parabolic and hyperbolic ) which has a degenerate second order term. The analysis by the "vanishing viscosity" is made by a careful study of the phase boundaries and of the topological structure of the phase sets. At the end we provide the existence of a discontinuous travelling wave.
Pierangelo Marcati. "Weak solutions to a nonlinear partial differential equation of mixed type." Differential Integral Equations 9 (4) 827 - 848, 1996. https://doi.org/10.57262/die/1367969890