Abstract:  

We use the method of vanishing viscosity and the theory of compensated compactness to prove the existence of a global weak solution for a non-strictly hyperbolic system modeling repulsive chemotaxis when the L2 norm of initial data is sufficiently small. The existence of invariant regions and strictly convex entropy-entropy flux pairs satisfying suitable properties are exploited to obtain a priori estimates that are used to construct global viscous solutions and to study the limit of those solutions as the viscosity coefficient tends to zero.