Existence of traveling wave solutions of a hyperbolic system

Abstract

In thesis, we establish and prove the existence of traveling wave solutions of a hyperbolic system. This system has various applications in many fields, in particular, biological science, such as chemotactic movement of bacteria, aggregation of microglia in Alzheimer’s disease, tumor angiogenesis and reinforced random walkers, etc.. One of prominent phenomena is the propagating of traveling waves. Numerical simulations will be represented to illustrate the process of forming steadily wave propagation in those applications. In addition, open problems are proposed for further study.