Nonlinear Hyperbolic-parabolic System Modeling Some Biological Phenomena

Abstract

In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N=1, the global existence of the weak solution will be established by the bootstrap argument.