On the global generalized solvability of a chemotaxis model with signal absorption and logistic growth terms

TL;DR

This paper establishes the existence of generalized global solutions for a chemotaxis model with signal absorption and logistic growth in bounded domains, covering a wide range of parameters and initial data.

Contribution

It introduces a new solution concept and proves global solvability for the chemotaxis system with arbitrary positive parameters and initial data.

Findings

Existence of generalized global solutions in bounded domains.

Applicability to arbitrary positive parameters and initial conditions.

Extension of solvability results for chemotaxis models.

Abstract

Introducing a suitable solution concept, we show that in bounded smooth domains $\Omega\subset \mathbb{R}^n$, $n\ge 1$, the initial boundary value problem for the chemotaxis system \begin{align*} u_t&=\Delta u -\chi\nabla\cdot\left(\frac{u}{v}\nabla v\right)+\kappa u -\mu u^2,\\ v_t&=\Delta v -uv, \end{align*} with homogeneous Neumann boundary conditions and widely arbitrary initial data has a generalized global solution for any $\mu, \kappa, \chi >0$.