High amplitude solutions for small data in systems of two conservation laws that change type

Dan Marchesin | Matos, Vitor

Keywords: Riemann problems | conservation laws | mixed type | non local 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 Shearer and Schaeffer classification. The viscosity matrix is the identity so the DRS point 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 DRS point. 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 studied by Dumortier, Roussarie and Sotomaior.

Anexos:

• High-12-19-d.pdf