Threshold for shock formation in the hyperbolic Keller-Segel model. (English) Zbl 1330.35250
Summary: We identify a sub-threshold for finite time shock formation in solutions to the one-dimensional hyperbolic Keller-Segel model. The main result states that under some assumptions on the initial potential, if the slope of the initial density is above a threshold at even one location, the solution must become discontinuous in finite time.
MSC:
| 35L67 | Shocks and singularities for hyperbolic equations |
| 35L60 | First-order nonlinear hyperbolic equations |
| 92C17 | Cell movement (chemotaxis, etc.) |
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