A Hamilton-Jacobi approach for a model of population structured by space and trait

By Emeric Bouin, Sepideh Mirrahimi. 2013

47 citations recorded by the source corpus.

We study a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable x 2 Rd and a phenotypical trait 2 . Considering diffusion, mutations and space-local competition between the individuals, we analyze the asymptotic (long- time/long-range in the x variable) exponential behavior of the solutions. Using some kind of real phase WKB ansatz, we prove that the propagation of the population in space can be described by a Hamilton-Jacobi equation with obstacle which is independent of . The effective Hamiltonian is derived from an eigenvalue problem. The main difficulties are the lack of regularity estimates in the space variable, and the lack of comparison principle due to the non-local term.

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

View Paper: https://www.semanticscholar.org/paper/b0efb7393c2c8f9d3b962f3561d20f6cee7371d8

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.”