Travelling Waves in a Nonlocal Reaction-Diffusion Equation as a Model for a Population Structured by a Space Variable and a Phenotypic Trait

By Matthieu Alfaro, Jérôme Coville, Gaël Raoul. 2012

86 citations recorded by the source corpus.

We consider a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypic trait. To sustain the possibility of invasion in the case where an underlying principal eigenvalue is negative, we investigate the existence of travelling wave solutions. We identify a minimal speed c* > 0, and prove the existence of waves when c ≥ c* and the nonexistence when 0 ≤ c < c*.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/6b26bcdfb7df10a6a28bf060437cd1225ef337e7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Genetics

1. Lenya Ryzhik
2. Emeric Bouin
3. Michael Winkler

In Modeling and Simulation

1. Lenya Ryzhik
2. Emeric Bouin
3. Michael Winkler
4. Youshan Tao

In Public Health, Environmental and Occupational Health

1. Lenya Ryzhik
2. Emeric Bouin
3. Michael Winkler
4. Youshan Tao

Citations in the corpus

• Super-linear spreading in local and non-local cane toads equations (2015, background): “Models involving non-local reaction terms have been the subject of intense study in recent years due to the complexity of the dynamics – see, for example, [2,11,17,25,30,31] and references therein.”