Analysis for a system of coupled reaction-diffusion parabolic equations arising in biology
type: Item
instance of: scholarly article
title: Analysis for a system of coupled reaction-diffusion parabolic equations arising in biology
zbMATH Open document ID: 0861.35038
DOI: 10.1016/0898-1221(96)00120-4
author: A. Boy
publication date: 1996-12-19T00:00:00Z
review text: The author investigates a model which describes the movement of the single-cell amoebae towards the region of relatively high concentration of a chemical which is produced by the amoebae themselves (the ``chemotaxis'' phenomen). It is considered the system \[ {\partial u\over\partial t}-d_1\Delta u=-\text{div}(u\nabla\psi(a)),\;{\partial a\over\partial t}-d_2\Delta a+k_2a=k_1u\quad\text{in }]0,T[\times\Omega, \] \[ {\partial u\over\partial n}-u {\partial\psi(a)\over\partial n}=0,\;{\partial a\over\partial n}=0\quad\text{on }\Gamma=\partial\Omega, \] \[ u(0,\cdot)=u_0,\;a(0,\cdot)= a_0\quad\text{in }\Omega, \] where \(\Omega\) is a smoothly bounded domain in \(\mathbb{R}^3\), \(u\) and \(a\) represent the population density and chemical concentration, respectively, \(\psi\) is a Lipschitzian function in \(\mathbb{R}\), \(d_1\), \(d_2\) are positive diffusion coefficients, \(d_1<d_2\), and \(k_1\), \(k_2\) are positive constants. In the general case the local existence and uniqueness of the solution is proved and in particular cases, for every fixed \(T>0\), global existence and uniqueness on \([0,T]\times\Omega\).
reviewed by: Ion Onciulescu
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35A07
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92E20
zbMATH DE Number: 950646
zbMATH Keywords: chemotaxis
Wikidata QID: Q113881642
MaRDI profile type: Publication
full work available at URL: 0898-1221(96)00120-4
OpenAlex ID: W1991689065
cites work: Q3994920
cites work: Q3890476
cites work: On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
cites work: Global existence of solutions for a strongly coupled quasilinear parabolic system
cites work: Q3706042
cites work: A method of coupling non‐linear hyperbolic systems: examples in CFD and plasma physics
cites work: Q5593959
cites work: Q5562267
cites work: Q4748596
cites work: Q4054616
cites work: Q5890172
cites work: Q5549989
cites work: Biased random walk models for chemotaxis and related diffusion approximations
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 950646