A kinetic chemotaxis model with internal states and temporal sensing

TL;DR

This paper develops a mathematical model for chemotaxis incorporating internal states and temporal sensing, proving the existence of solutions and analyzing the system's behavior in one dimension.

Contribution

It introduces a novel kinetic chemotaxis model with internal states and temporal gradient, providing rigorous analysis of solutions and hydrodynamic limits.

Findings

Established global existence of solutions

Derived hydrodynamic limit in one dimension

Used Fourier transform for key a priori estimates

Abstract

By employing the Fourier transform to derive key a priori estimates for the temporal gradient of the chemical signal, we establish the existence of global solutions and hydrodynamic limit of a chemotactic kinetic model with internal states and temporal gradient in one dimension, which is a system of two transport equations coupled to a parabolic equation proposed in [4].