Large Viscous Solutions for Small Data in Systems of Conservation Laws that Change Type

Dan Marchesin | Matos, Vitor

Keywords: Riemann problems; conservation laws; mixed type; viscous profile; nonlocal solution

We study a quadratic system of conservation laws with an elliptic region. The second order terms in the fluxes correspond to type IV in Schaeffer and Shearer classification. There exists a special singularity for the EDOs associated to traveling waves for shocks. In our case, this singularity lies on the elliptic boundary. We prove that high amplitude Riemann solutions arise from Riemann data with arbitrarily small amplitude in the hyperbolic region near the special singularity. For such Riemann data there is no small amplitude solution. This behavior is related to the bifurcation of one of the codimension-3 nilpotent singularities of planar ODEs studied by Dumortier, Roussarie and Sotomaior.

Anexos:

• LVS-MM.pdf