8 citations · 43 across the 16 of their papers we have counts for
16 papers
Spreading properties of the Fisher--KPP equation when the intrinsic growth rate is maximal in a moving patch of bounded size
Thomas Giletti, Léo Girardin, Hiroshi Matano
This paper is concerned with spreading properties of space-time heterogeneous Fisher--KPP equations in one space dimension. We focus on the case of everywhere favorable environment…
Propagation dynamics of solutions to spatially periodic reaction-diffusion systems with hybrid nonlinearity
Quentin Griette, Hiroshi Matano
In this paper we investigate the dynamical properties of a spatially periodic reaction-diffusion system {whose reaction terms are of hybrid nature in the sense that they are partly…
Asymptotic behavior of fronts and pulses of the bidomain model
Hiroshi Matano, Yoichiro Mori, Mitsunori Nara +1
The bidomain model is the standard model for cardiac electrophysiology. In this paper, we investigate the instability and asymptotic behavior of planar fronts and planar pulses of…
Dynamics of time-periodic reaction-diffusion equations with front-like initial data on
Weiwei Ding, Hiroshi Matano
This paper is concerned with the Cauchy problem where is a rather general nonli…
Spreading speeds for multidimensional reaction-diffusion systems of the prey-predator type
Arnaud Ducrot, Thomas Giletti, Hiroshi Matano
We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading prope…
Existence and uniqueness of propagating terraces
Thomas Giletti, Hiroshi Matano
This work focuses on dynamics arising from reaction-diffusion equations , where the profile of propagation is no longer characterized by a single front, but by a layer of several f…
Generation of fine transition layers and their dynamics for the stochastic Allen--Cahn equation
Matthieu Alfaro, Dimitra Antonopoulou, Georgia Karali +1
We study an $\ep$-dependent stochastic Allen--Cahn equation with a mild random noise on a bounded domain in , . Here $\ep$ is a small positive parameter that…
Dynamics of Time-Periodic Reaction-Diffusion Equations with Compact Initial Support on R
Weiwei Ding, Hiroshi Matano
This paper is concerned with the asymptotic behavior of bounded solutions of the Cauchy problem \begin{equation*} \left\{ \begin{array}{ll} u_t=u_{xx} +f(t,u), & x\in\mathbb{R},\,t…
Radial terrace solutions and propagation profile of multistable reaction-diffusion equations over
Yihong Du, Hiroshi Matano
We study the propagation profile of the solution to the nonlinear diffusion problem , , where $…
On the large time behavior of the solutions of a nonlocal ordinary differential equation with mass conservation
Danielle Hilhorst, Hiroshi Matano, Thanh Nam Nguyen +1
We consider an initial value problem for a nonlocal differential equation with a bistable nonlinearity in several space dimensions. The equation is an ordinary differential equatio…
Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations
Arnaud Ducrot, Thomas Giletti, Hiroshi Matano
We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities (including multistable ones) and study the asymptotic behavior of so…
On the validity of formal asymptotic expansions in Allen-Cahn equation and FitzHugh-Nagumo system with generic initial data
Matthieu Alfaro, Hiroshi Matano
Formal asymptotic expansions have long been used to study the singularly perturbed Allen-Cahn type equations and reaction-diffusion systems, including in particular the FitzHugh-Na…
A variational problem associated with the minimal speed of travelling waves for spatially periodic reaction-diffusion equations
Xing Liang, Xiaotao Lin, Hiroshi Matano
We consider the equation where is a nonnegative measure on that is periodic in In the case where is a smoot…
Maximizing the spreading speed of KPP fronts in two-dimensional stratified media
Xing Liang, Xiaotao Lin, Hiroshi Matano
We consider the equation , with monostable nonliearity, where is a nonnegative measure on that is periodic…
Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation
Matthieu Alfaro, Harald Garcke, Danielle Hilhorst +2
We study the singular limit of a spatially inhomogeneous and anisotropic reaction-diffusion equation. We use a Finsler metric related to the anisotropic diffusion term and work in…
The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system
Matthieu Alfaro, Danielle Hilhorst, Hiroshi Matano
We consider an Allen-Cahn type equation with a bistable nonlinearity associated to a double-well potential whose well-depths can be slightly unbalanced, and where the coefficient o…