A relation between cross-diffusion and reaction-diffusion

Hideki Murakawa

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Reaction-diffusion system approximations to a cross-diffusion system are investigated. Iida and Ninomiya [Recent Advances on Elliptic and Parabolic Issues, 145-164 (2006)] proposed a semilinear reaction-diffusion system with a small parameter and showed that the limit equation takes the form of a weakly coupled cross-diffusion system provided that solutions of both the reaction-diffusion and the cross-diffusion systems are sufficiently smooth. In this paper, the results are extended to a more general cross-diffusion problem involving strongly coupled systems. It is shown that a solution of the problem can be approximated by that of a semilinear reaction-diffusion system without any assumptions on the solutions. This indicates that the mechanism of cross-diffusion might be captured by reaction-diffusion interaction.

Original languageEnglish
Pages (from-to)147-158
Number of pages12
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume5
Issue number1
DOIs
Publication statusPublished - Feb 1 2012

Fingerprint

Cross-diffusion System
Cross-diffusion
Reaction-diffusion
Reaction-diffusion System
Semilinear Systems
Coupled System
Diffusion Problem
Small Parameter
Approximation
Interaction

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

A relation between cross-diffusion and reaction-diffusion. / Murakawa, Hideki.

In: Discrete and Continuous Dynamical Systems - Series S, Vol. 5, No. 1, 01.02.2012, p. 147-158.

Research output: Contribution to journalArticle

@article{aec4ff8b88cb485da2d6d943da2c0131,
title = "A relation between cross-diffusion and reaction-diffusion",
abstract = "Reaction-diffusion system approximations to a cross-diffusion system are investigated. Iida and Ninomiya [Recent Advances on Elliptic and Parabolic Issues, 145-164 (2006)] proposed a semilinear reaction-diffusion system with a small parameter and showed that the limit equation takes the form of a weakly coupled cross-diffusion system provided that solutions of both the reaction-diffusion and the cross-diffusion systems are sufficiently smooth. In this paper, the results are extended to a more general cross-diffusion problem involving strongly coupled systems. It is shown that a solution of the problem can be approximated by that of a semilinear reaction-diffusion system without any assumptions on the solutions. This indicates that the mechanism of cross-diffusion might be captured by reaction-diffusion interaction.",
author = "Hideki Murakawa",
year = "2012",
month = "2",
day = "1",
doi = "10.3934/dcdss.2012.5.147",
language = "English",
volume = "5",
pages = "147--158",
journal = "Discrete and Continuous Dynamical Systems - Series S",
issn = "1937-1632",
publisher = "American Institute of Mathematical Sciences",
number = "1",

}

TY - JOUR

T1 - A relation between cross-diffusion and reaction-diffusion

AU - Murakawa, Hideki

PY - 2012/2/1

Y1 - 2012/2/1

N2 - Reaction-diffusion system approximations to a cross-diffusion system are investigated. Iida and Ninomiya [Recent Advances on Elliptic and Parabolic Issues, 145-164 (2006)] proposed a semilinear reaction-diffusion system with a small parameter and showed that the limit equation takes the form of a weakly coupled cross-diffusion system provided that solutions of both the reaction-diffusion and the cross-diffusion systems are sufficiently smooth. In this paper, the results are extended to a more general cross-diffusion problem involving strongly coupled systems. It is shown that a solution of the problem can be approximated by that of a semilinear reaction-diffusion system without any assumptions on the solutions. This indicates that the mechanism of cross-diffusion might be captured by reaction-diffusion interaction.

AB - Reaction-diffusion system approximations to a cross-diffusion system are investigated. Iida and Ninomiya [Recent Advances on Elliptic and Parabolic Issues, 145-164 (2006)] proposed a semilinear reaction-diffusion system with a small parameter and showed that the limit equation takes the form of a weakly coupled cross-diffusion system provided that solutions of both the reaction-diffusion and the cross-diffusion systems are sufficiently smooth. In this paper, the results are extended to a more general cross-diffusion problem involving strongly coupled systems. It is shown that a solution of the problem can be approximated by that of a semilinear reaction-diffusion system without any assumptions on the solutions. This indicates that the mechanism of cross-diffusion might be captured by reaction-diffusion interaction.

UR - http://www.scopus.com/inward/record.url?scp=80051970149&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051970149&partnerID=8YFLogxK

U2 - 10.3934/dcdss.2012.5.147

DO - 10.3934/dcdss.2012.5.147

M3 - Article

AN - SCOPUS:80051970149

VL - 5

SP - 147

EP - 158

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

SN - 1937-1632

IS - 1

ER -