### Abstract

We consider a type of singular limit problem called the fast reaction limit. The problem of the fast reaction limit involves studying the behaviour of solutions of reaction–diffusion systems when the reaction speeds are very fast. Fast reaction limits of two-component systems have been studied in recent decades. In most of these systems, the fast reaction terms of each component are represented by the same function. Fast reaction limits of systems with different fast reaction terms are still far from being well understood. In this paper, we focus on a reaction–diffusion system for which the reaction terms consist of monomial functions of various powers. The behaviour of interfaces arising in the fast reaction limit of this system is studied. Depending on the powers, three types of behaviour are observed: (i) the initial interface vanishes instantaneously, (ii) the interface propagates at a finite speed, and (iii) the interface does not move.

Original language | English |
---|---|

Pages (from-to) | 2715-2735 |

Number of pages | 21 |

Journal | Journal of Differential Equations |

Volume | 263 |

Issue number | 5 |

DOIs | |

Publication status | Published - Sep 5 2017 |

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### Keywords

- Fast reaction limit
- Free boundary problem
- Reaction–diffusion system
- Singular limit problem

### ASJC Scopus subject areas

- Analysis

### Cite this

*Journal of Differential Equations*,

*263*(5), 2715-2735. https://doi.org/10.1016/j.jde.2017.04.009

**Vanishing, moving and immovable interfaces in fast reaction limits.** / Iida, M.; Monobe, Harunori; Murakawa, H.; Ninomiya, H.

Research output: Contribution to journal › Article

*Journal of Differential Equations*, vol. 263, no. 5, pp. 2715-2735. https://doi.org/10.1016/j.jde.2017.04.009

}

TY - JOUR

T1 - Vanishing, moving and immovable interfaces in fast reaction limits

AU - Iida, M.

AU - Monobe, Harunori

AU - Murakawa, H.

AU - Ninomiya, H.

PY - 2017/9/5

Y1 - 2017/9/5

N2 - We consider a type of singular limit problem called the fast reaction limit. The problem of the fast reaction limit involves studying the behaviour of solutions of reaction–diffusion systems when the reaction speeds are very fast. Fast reaction limits of two-component systems have been studied in recent decades. In most of these systems, the fast reaction terms of each component are represented by the same function. Fast reaction limits of systems with different fast reaction terms are still far from being well understood. In this paper, we focus on a reaction–diffusion system for which the reaction terms consist of monomial functions of various powers. The behaviour of interfaces arising in the fast reaction limit of this system is studied. Depending on the powers, three types of behaviour are observed: (i) the initial interface vanishes instantaneously, (ii) the interface propagates at a finite speed, and (iii) the interface does not move.

AB - We consider a type of singular limit problem called the fast reaction limit. The problem of the fast reaction limit involves studying the behaviour of solutions of reaction–diffusion systems when the reaction speeds are very fast. Fast reaction limits of two-component systems have been studied in recent decades. In most of these systems, the fast reaction terms of each component are represented by the same function. Fast reaction limits of systems with different fast reaction terms are still far from being well understood. In this paper, we focus on a reaction–diffusion system for which the reaction terms consist of monomial functions of various powers. The behaviour of interfaces arising in the fast reaction limit of this system is studied. Depending on the powers, three types of behaviour are observed: (i) the initial interface vanishes instantaneously, (ii) the interface propagates at a finite speed, and (iii) the interface does not move.

KW - Fast reaction limit

KW - Free boundary problem

KW - Reaction–diffusion system

KW - Singular limit problem

UR - http://www.scopus.com/inward/record.url?scp=85018977687&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018977687&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2017.04.009

DO - 10.1016/j.jde.2017.04.009

M3 - Article

VL - 263

SP - 2715

EP - 2735

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 5

ER -