American Institute of Mathematical Sciences

March 2018, 13(1): 119-153. doi: 10.3934/nhm.2018006

Fisher-KPP equations and applications to a model in medical sciences

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

Received  August 2016 Revised  January 2018 Published  March 2018

Fund Project: This work has been carried out in the framework of Archimedes LabEx (ANR-11-LABX-0033) and of the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the "Investissements d'Avenir' French Government program managed by the French National Research Agency (ANR). The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n.321186 - ReaDi - Reaction-Diffusion Equations, Propagation and Modelling, and from the ANR project NONLOCAL (ANR-14-CE25-0013).

This paper is devoted to a class of reaction-diffusion equations with nonlinearities depending on time modeling a cancerous process with chemotherapy. We begin by considering nonlinearities periodic in time. For these functions, we investigate equilibrium states, and we deduce the large time behavior of the solutions, spreading properties and the existence of pulsating fronts. Next, we study nonlinearities asymptotically periodic in time with perturbation. We show that the large time behavior and the spreading properties can still be determined in this case.

Citation: Benjamin Contri. Fisher-KPP equations and applications to a model in medical sciences. Networks & Heterogeneous Media, 2018, 13 (1) : 119-153. doi: 10.3934/nhm.2018006
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