Related papers: Reaction-diffusion equations in the half-space
In this paper, Lyapunov-Razumikhin technique, design of state-dependent switching laws, a fixed point theorem and variational methods are employed to derive the existence and the unique existence results of globally exponentially stable…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
To better understand how populations respond to dynamic external pressure, we propose a new diffusion model in the moving half-line {z $\ge$ b(t)}, where the boundary position b(t) is a given nondecreasing function of time. A Robin boundary…
This work contributes to an understanding of the domain size's effect on the existence and uniqueness of the linear convection--diffusion equation with integral-type boundary conditions, where boundary conditions depend non-locally on…
This paper addresses the derivation of generic and tractable sufficient conditions ensuring the stability of a coupled system composed of a reaction-diffusion partial differential equation (PDE) and a finite-dimensional linear time…
In this review, we provide a concise summary of several important mathematical results for stochastic travelling waves generated by monostable and bistable reaction-diffusion stochastic partial differential equations (SPDEs). In particular,…
A reaction-diffusion model which is called the field-road model was introduced by Berestycki, Roquejoffre and Rossi [9] to describe biological invasion with fast diffusion on a line. In this paper, we investigate this model in a…
We establish in this article spreading properties for the solutions of equations of the type $\partial$ t u -- a(x)$\partial$ xx u -- q(x)$\partial$ x u = f (x, u), where a, q, f are only assumed to be uniformly continuous and bounded in x,…
We consider quasi-stationary (travelling wave type) solutions to a general nonlinear reaction-convection-diffusion equation with arbitrary, autonomous coefficients. The second order nonlinear equation describing one dimensional travelling…
This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established.…
We study analytically and numerically a bistable reaction-diffusion equation on an arbitrary finite network. We prove that stable fixed points (multi-fronts) exist for any configuration as long as the diffusion is small. We also study fold…
We consider a multidimensional reaction-diffusion equation of either ignition or monostable type, involving periodic heterogeneity, and analyze the dependence of the propagation phenomena on the direction. We prove that the (minimal) speed…
This paper focuses on propagation phenomena in reaction-diffusion equations with a weaklymonostable nonlinearity. The reaction term can be seen as an intermediate between the classicallogistic one (or Fisher-KPP) and the standard weak Allee…
We consider a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypical trait. To sustain the possibility of invasion in the case where an underlying principal eigenvalue is negative,…
We consider positive travelling fronts of the time-delayed reaction-diffusion equation with the monostable birth function. Our main result says that for every fixed and sufficiently large velocity c, the positive travelling front is unique…
In this paper,under an abstract setting we establish the existence of spatially inhomogeneous steady states and the asymptotic propagation properties for a large class of monotone evolution systems without spatial translation invariance.…
This paper analyzes the stability of a reactiondiffusion equation coupled with a finite-dimensional controller through Dirichlet boundary input and Neumann boundary output. Going against the flow, we intend to propose numerical certificates…
We give a complete characterization of the boundary traces $\varphi_i$ ($i=1,\dots,K$) supporting spiraling waves, rotating with a given angular speed $\omega$, which appear as singular limits of competition-diffusion systems of the type \[…
We consider a scalar parabolic equation in one spatial dimension. The equation is constituted by a convective term, a reaction term with one or two equilibria, and a positive diffusivity which can however vanish. We prove the existence and…
The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence…