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

Benjamin Contri

doi:10.3934/nhm.2018006

Article Contents

2018, Volume 13, Issue 1: 119-153. Doi: 10.3934/nhm.2018006

This issue Previous Article On Lennard-Jones systems with finite range interactions and their asymptotic analysis Next Article Green's function for elliptic systems: Moment bounds

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

Benjamin Contri

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

Received: July 31, 2016

Revised: December 31, 2017

Published: March 2018

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).

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K57, 92C50; Secondary: 35C07.

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