Global solutions of nonlinear transport equations for chemosensitive movement. (English) Zbl 1099.82018

Hwang, Hyung Ju; Kang, Kyungkeun; Stevens, Angela

SIAM J. Math. Anal. 36, No. 4, 1177-1199 (2005).

Summary: A widespread phenomenon in moving microorganisms and cells is their ability to reorient themselves depending on changes of concentrations of certain chemical signals. In this paper we discuss kinetic models for chemosensitive movement, which also takes into account evaluations of gradient fields of chemical stimuli which subsequently influence the motion of the respective microbiological species. So far in the rigorous derivations, only the density of the chemo-attractant was supposed to influence the motion of the chemosensitive species. Here we show that in the macroscopic limit some types of evaluations of gradient fields of the chemical stimulus result in a change of the classical parabolic Keller–Segel model for chemotaxis. Under suitable structure conditions, global solutions for the kinetic models can be shown.

MSC:

82C70	Transport processes in time-dependent statistical mechanics
35K55	Nonlinear parabolic equations
45K05	Integro-partial differential equations
92C17	Cell movement (chemotaxis, etc.)
35K50	Systems of parabolic equations, boundary value problems (MSC2000)

Keywords:

sensing of gradient fields; global solutions; drift-diffusion limit; Keller-Segel model