## Wave breaking in a class of non-local conservation laws

- April 5, 2019
- 2:30 p.m.
- LeConte 317R

## Abstract

In this talk, we discuss threshold conditions for wave breaking in a class of non-local conservation law with concavity changing flux. From a class of non-local conservation laws, the Riccati-type ODE system that governs a solutionâ€™s gradient is obtained. The changes in concavity of the flux correspond to the sign changes in the leading coefficient functions of the ODE system. We identify the blow-up condition of this structurally generalized Riccati-type ODE. The method is illustrated via the Whitham-type equation with nonlinear drift and the traffic flow models with nonlocal-concave-convex flux.