From the 2 of 9 linked papers with an AI index.
9 papers
Propagation phenomena in KPP-bistable periodic patchy environments
Quentin Griette, François Hamel, Mingmin Zhang +1
This paper first investigates the propagation dynamics of solutions to the Cauchy problem for a one-dimensional reaction-diffusion equation in a spatially periodic environment cons…
On advective nonlocal operators: multiplicity of principal eigenpairs
Arnaud Ducrot, Quentin Griette, Xing Liang
We study the existence and multiplicity of principal eigenvalues and eigenfunctions for a periodically heterogeneous nonlocal dispersal model with advection. The operator we consid…
Propagation dynamics of an acid-mediated invasion model with degenerate tumor diffusion
Xinyue Cao, Quentin Griette, Xiong Li +1
The paper proves the existence of traveling wave fronts in an acid-mediated tumor invasion model with density‑dependent degenerate diffusion, using a variable transformation and an…
Front propagation in hybrid reaction-diffusion epidemic models with spatial heterogeneity. Part II: Pulsating traveling waves
Quentin Griette, Hiroshi Matano
The paper proves the existence of pulsating traveling wave solutions for a two‑species reaction‑diffusion epidemic model in a periodic environment, showing that such waves exist fo…
Sharp threshold dynamics for a bistable age-structured population model
Quentin Griette, Franco Herrera
This paper is devoted to the long-term dynamics of solutions to the Gurtin-MacCamy population model with a bistable birth function. We consider a one-parameter monotone family of i…
Front propagation into unstable states for periodic monotone reaction-diffusion systems
Liangliang Deng, Arnaud Ducrot, Quentin Griette
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that con…