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

Benjamin Contri; Benjamin Contri

doi:10.3934/nhm.2018006

Networks and Heterogeneous Media

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

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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: 01 August 2016 Revised: 01 January 2018
Primary: 35K57, 92C50; Secondary: 35C07

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.
- Reaction-diffusion equation,
- KPP nonlinearity,
- principal eigenvalue,
- pulsating front,
- spreading speed,
- medical models
Citation: Benjamin Contri. 2018: Fisher-KPP equations and applications to a model in medical sciences, Networks and Heterogeneous Media, 13(1): 119-153. doi: 10.3934/nhm.2018006

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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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