Critical threshold phenomena in a mixed-type system of conservation laws modeling attractive chemotaxis

This paper is concerned with the critical threshold phenomena associated with the Cauchy problem for a mixed-type one-dimensional system of conservation laws modeling attractive chemotaxis. We prove the global existence of a unique C1 solution in the strictly hyperbolic region under certain conditions on the composition of the eigenvalues and the initial data. We also show that if these conditions are violated, there is a finite time such that slopes of the solution become unbounded as the life span of the solution is approached.