### Impacto

### Downloads

Downloads per month over past year

Esquinas, J. and Herrero, Miguel A.
(1990)
*Travelling wave solutions to a semilinear diffusion system.*
Siam Journal on Mathematical Analysis , 21
(1).
pp. 123-136.
ISSN 0036-1410

Official URL: http://epubs.siam.org/action/showAbstract?page=123&volume=21&issue=1&journalCode=sjmaah

## Abstract

We consider the semilinear system (S) ut−uxx+vp=0, vt−vxx+uq=0(−∞<x<+∞,t>0) with p>0 and q>0. We seek nonnegative and nontrivial travelling wave solutions to (S): u(x,t)=φ(ct−x), v(x,t)=ψ(ct−x) possessing sharp fronts, i.e., such that φ(ξ)=ψ(ξ)=0 for ξ≤ξ0 and some finite ξ0, which after a phase shift can always be assumed to be located at the origin. These solutions are called finite travelling waves (FTW). Here we show that if pq<1, for any real c there exists an FTW that is unique up to phase translations and unbounded, whereas no FTW exists if pq≥1. The asymptotic wave profiles near the front as well as far from it are also determined.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Semilinear diffusion systems; travelling waves; fronts; asymptotic behaviour; travelling wave solutions; existence; uniqueness; nonexistence |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 18091 |

Deposited On: | 31 Jan 2013 09:21 |

Last Modified: | 12 Dec 2018 15:08 |

### Origin of downloads

Repository Staff Only: item control page