This site uses cookies. By continuing to use this site you agree to our use of cookies. To find out more, see our Privacy and Cookies policy.
Paper

On the nonlocal Fisher–KPP equation: steady states, spreading speed and global bounds

and

Published 14 October 2014 • © 2014 IOP Publishing Ltd & London Mathematical Society
, , Citation François Hamel and Lenya Ryzhik 2014 Nonlinearity 27 2735 DOI 10.1088/0951-7715/27/11/2735

Download Article PDF

Article metrics

540 Total downloads

Share this article

Author e-mails

ryzhik@math.stanford.edu

Author affiliations

1 Aix Marseille Université, CNRS, Centrale Marseille, Institut de Mathématiques de Marseille, UMR 7373, 13453 Marseille, France, and Institut Universitaire de France

2 Department of Mathematics, Stanford University, Stanford, CA 94305, USA

Dates

  1. Received 10 July 2013
  2. Accepted 11 September 2014
  3. Published

Buy this article in print

Journal RSS
Sign up for new issue notifications
0951-7715/27/11/2735

Abstract

We consider the Fisher–KPP (for Kolmogorov–Petrovsky–Piskunov) equation with a nonlocal interaction term. We establish a condition on the interaction that allows for existence of non-constant periodic solutions, and prove uniform upper bounds for the solutions of the Cauchy problem, as well as upper and lower bounds on the spreading rate of the solutions with compactly supported initial data.

Export citation and abstract BibTeX RIS

Previous article in issue
Next article in issue

Recommended by J Lega

10.1088/0951-7715/27/11/2735