Travelling wave solutions for some models in phytopathology

Jean Baptiste Burie (1, 2) , Arnaud Ducrot (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics

In this work several models of fungal disease propagation are considered. They consist of reaction-diffusion systems coupled with ordinary differential equations with or without time delay as well as integro-differential system of equations. We derive some conditions that ensure the existence and uniqueness of travelling wave solutions for these various models. Our proof is based on a suitable re-formulation in the form of a nonlinear integral equation with measure kernel convolutions.

Domains: Analysis of PDEs [math.AP]

Jean Baptiste Burie, Arnaud Ducrot. Travelling wave solutions for some models in phytopathology. Nonlinear Analysis: Real World Applications, 2009, 10, pp.2307-2325. ⟨10.1016/j.nonrwa.2008.04.013⟩. ⟨hal-00293372⟩