Sharp interface limit of the Fisher-KPP equation when initial data have slow exponential decay
DUCROT, Arnaud
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]
Institut de Mathématiques de Bordeaux [IMB]
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]
Institut de Mathématiques de Bordeaux [IMB]
DUCROT, Arnaud
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
Discrete and Continuous Dynamical Systems - Series B. 2011p. 16 (2011), 15-29.
American Institute of Mathematical Sciences
English Abstract
We investigate the singular limit, as $\ep \to 0$, of the Fisher equation $\partial _t u=\ep \Delta u + \ep ^{-1}u(1-u)$ in the whole space. We consider initial data with compact support plus perturbations with {\it slow ...Read more >
We investigate the singular limit, as $\ep \to 0$, of the Fisher equation $\partial _t u=\ep \Delta u + \ep ^{-1}u(1-u)$ in the whole space. We consider initial data with compact support plus perturbations with {\it slow exponential decay}. We prove that the sharp interface limit moves by a constant speed, which dramatically depends on the tails of the initial data. By performing a fine analysis of both the generation and motion of interface, we provide a new estimate of the thickness of the transition layers.Read less <
Origin
Hal imported