Journal of the
Korean Mathematical Society JKMS

This paper considers a parabolic-hyperbolic-hyperbolic type chemotaxis system in $\mathbb{R}^{d}$, $d\ge3$, describing tumor-induced angiogenesis. The global existence result and temporal decay estimate for a unique mild solution are established under the assumption that some Sobolev norms of initial data are sufficiently small.

Keywords: Anderson-Chaplain model, angiogenesis, temporal decay

MSC numbers: Primary 35Q92, 35M31, 92C17

Supported by: The first author was supported by National Research Foundation (NRF) of Korea (Grant no. NRF-2021R1F1A1064209).