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pro vyhledávání: '"Hamel, François"'
We consider a bistable reaction-diffusion equation $u_t=\Delta u +f(u)$ on $\mathbb{R}^N$ in the presence of an obstacle $K$, which is a wall of infinite span with many holes. More precisely, $K$ is a closed subset of $\mathbb{R}^N$ with smooth bound
Externí odkaz:
http://arxiv.org/abs/2406.04688
Autor:
Hamel, François, Russ, Emmanuel
We prove a Faber-Krahn inequality for the Laplacian with drift under Robin boundary condition, provided that the $\beta$ parameter in the Robin condition is large enough. The proof relies on a compactness argument, on the convergence of Robin eigenva
Externí odkaz:
http://arxiv.org/abs/2405.12148
Autor:
Hamel, François, Karakhanyan, Aram
Steady incompressible potential flows of an inviscid or viscous fluid are considered in infinite N-dimensional cylinders with tangential boundary conditions. We show that such flows, if away from stagnation, are constant and parallel to the direction
Externí odkaz:
http://arxiv.org/abs/2312.02571
Autor:
Hamel, François, Zhang, Mingmin
This paper is concerned with the existence of transition fronts for a one-dimensional twopatch model with KPP reaction terms. Density and flux conditions are imposed at the interface between the two patches. We first construct a pair of suitable supe
Externí odkaz:
http://arxiv.org/abs/2307.13307
Autor:
Hamel, François, Rossi, Luca
This paper is concerned with the large-time dynamics of bounded solutions of reaction-diffusion equations with bounded or unbounded initial support in R N. We start with a survey of some old and recent results on the spreading speeds of the solutions
Externí odkaz:
http://arxiv.org/abs/2307.03555
Publikováno v:
Discrete and Continuous Dynamical Systems - Series S, 2024, 17 (4), pp.1460-1484
In this paper, we investigate the large-time behavior of bounded solutions of the Cauchy problem for a reaction-diffusion equation in $\mathbb{R}^N$ with bistable reaction term. We consider initial conditions that are chiefly indicator functions of b
Externí odkaz:
http://arxiv.org/abs/2304.00828
Autor:
Hamel, François, Rossi, Luca
We consider reaction-diffusion equations $\partial_tu=\Delta u+f(u)$ in the whole space $\mathbb{R}^N$ and we are interested in the large-time dynamics of solutions ranging in the interval $[0,1]$, with general unbounded initial support. Under the hy
Externí odkaz:
http://arxiv.org/abs/2207.05999
Autor:
Hamel, François, Rossi, Luca
Let $u$ be a solution of the Fisher-KPP equation $$ \partial_t u=\Delta u+f(u),\quad t>0,\ x\in\mathbb{R}^N. $$ We address the following question: does $u$ become locally planar as $t\to+\infty$ ? Namely, does $u(t_n,x_n+\cdot)$ converge locally unif
Externí odkaz:
http://arxiv.org/abs/2207.05147
We consider reaction-diffusion fronts in spatially periodic bistable media with large periods. Whereas the homogenization regime associated with small periods had been well studied for bistable or Fisher-KPP reactions and, in the latter case, a formu
Externí odkaz:
http://arxiv.org/abs/2204.09301
We consider a three-species predator-prey system involving two competing predators and one prey. The species diffuse with nonlocal dispersal kernels with possibly non-compact support, and they interact in a heterogeneous environment moving with a pos
Externí odkaz:
http://arxiv.org/abs/2202.08089