A parabolic-elliptic chemo-repulsion system in 2D domains with nonlinear production

Abstract

In this paper we analyze a parabolic-elliptic chemo-repulsion system with superlinear production term in two-dimensional domains. Under the injection extract chemical substance on a subdomain $\omega\subset\Omega\subset\mathbb{R}^2$, we prove the existence and uniqueness of global-in-time strong solutions at finite time.