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

Benjamin Contri (1, 2)

1 I2M - Institut de Mathématiques de Marseille
2 AMU - Aix Marseille Université

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.

Domaines: Equations aux dérivées partielles [math.AP]

Benjamin Contri. Fisher-KPP equations and applications to a model in medical sciences. 2016. ⟨hal-01331879⟩