Abstract
We identify sub-thresholds for finite time shock formation 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 solution's gradient is obtained. The changes in concavity of the flux function 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 traffic flow models with nonlocal-concave-convex flux. The techniques and ideas developed in this paper is applicable to a large class of non-local conservation laws.
| Original language | English |
|---|---|
| Pages (from-to) | 580-599 |
| Number of pages | 20 |
| Journal | Journal of Differential Equations |
| Volume | 266 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 5 2019 |
Keywords
- Blow up
- Critical threshold
- Look-ahead dynamics
- Nonconcave flux
- Nonlocal conservation law
- Shock formation
- Traffic flow