Related papers: Propagating interface in a monostable reaction-dif…
In this paper, we extend and complement previous works about propagation in kinetic reaction-transport equations. The model we study describes particles moving according to a velocity-jump process, and proliferating according to a reaction…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
In this paper, we study the problem of finding the solution of a multi-dimensional time fractional reactiondiffusion equation with nonlinear source from the final value data. We prove that the present problem is not well-posed. Then…
This paper is concerned with the asymptotic behavior of solutions of time periodic reaction-diffusion equation \begin{equation*}\label{aaa} \begin{cases} u_{t}(x,t)=u_{xx}(x,t)+f(t,u(x,t)),\quad \,\,\forall x\in\mathbb{R},\,t>0,\\…
In this paper, we investigate an initial-boundary-value problem of a reaction-diffusion equation in a bounded domain with a Robin boundary condition and introduce some particular parameters to consider the non-zero flux on the boundary.…
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \ge 3$. Combining this result with…
We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
In this paper, curved fronts are constructed for spatially periodic bistable reaction-diffusion equations under the a priori assumption that there exist pulsating fronts in every direction. Some sufficient and some necessary conditions of…
We prove uniqueness of a martingale problem with boundary conditions on a simplex associated to a differential operator with an unbounded drift. We show that the solution of the martingale problem remains absorbed at the boundary once it…
Self-interacting diffusions are processes living on a compact Riemannian manifold defined by a stochastic differential equation with a drift term depending on the past empirical measure of the process. The asymptotics of this measure is…
The question addressed here is the long time evolution of the solutions to a class of one-dimensional reaction-diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation, discussed in the first…
We extend the class of initial conditions for scalar delayed reaction-diffusion equations $u_t (t,x)=u_{xx}(t,x)+f(u(t, x), u(t-h, x))$ which evolve in solutions converging to monostable traveling waves. Our approach allows to compute, in…
In this paper, a distributed velocity-constrained consensus problem is studied for discrete-time multi-agent systems, where each agent's velocity is constrained to lie in a nonconvex set. A distributed constrained control algorithm is…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
We model the growth, dispersal and mutation of two phenotypes of a species using reaction-diffusion equations, focusing on the biologically realistic case of small mutation rates. After verifying that the addition of a small linear mutation…
This paper is devoted to the investigation of spatial spreading speeds and traveling wave solutions of monostable evolution equations with nonlocal dispersal in time and space periodic habitats. It has been shown in an earlier work by the…
With the aim to characterize the formation and propagation of bulges in cylindrical rubber balloons, we carry out an expansion of the non-linear axisymmetric membrane model assuming slow axial variations. We obtain a diffuse interface model…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
We investigate in this paper a scalar reaction diffusion equation with a nonlinear reaction term depending on x-ct. Here, c is a prescribed parameter modelling the speed of climate change and we wonder whether a population will survive or…