相关论文: The Bramson logarithmic delay in the cane toads eq…

In this paper, we study propagation in a nonlocal reaction-diffusion-mutation model describing the invasion of cane toads in Australia. The population of toads is structured by a space variable and a phenotypical trait and the…

In this paper, we show super-linear propagation in a nonlocal reaction-diffusion-mutation equation modeling the invasion of cane toads in Australia that has attracted attention recently from the mathematical point of view. The population of…

We consider a class of reaction-diffusion equations of Fisher-KPP type in which the nonlinearity (reaction term) $f$ is merely $C^1$ at $u=0$ due to a logarithmic competition term. We first derive the asymptotic behavior of (minimal speed)…

We investigate a general, local version of the cane toads equation, which models the spread of a population structured by unbounded motility. We use the thin-front limit approach of Evans and Souganidis in [Indiana Univ. Math. J., 1989] to…

We consider solutions of the KPP-type equations with a periodically varying reaction rate, and compactly supported initial data. It has been shown by M. Bramson in the case of the constant reaction rate that the lag between the position of…

We investigate the asymptotic speed of spread of the solutions of a non-autonomous Fisher-KPP equation with nonlocal diffusion, driven by a thin-tailed kernel. In this paper, we are concerned with both compactly supported and exponentially…

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…

This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory…

Incorporating free boundary into time-delayed reaction-diffusion equations yields a compatible condition that guarantees the well-posedness of the initial value problem. With the KPP type nonlinearity we then establish a vanishing-spreading…

In this paper, we study the influence of an Allee effect on the spreading rate in a local reaction-diffusion-mutation equation modelling the invasion of cane toads in Australia. We are, in particular, concerned with the case when the…

The famous Fisher-KPP reaction diffusion model combines linear diffusion with the typical Fisher-KPP reaction term, and appears in a number of relevant applications. It is remarkable as a mathematical model since, in the case of linear…

In this paper, we study the influence of the mortality trade-off in a nonlocal reaction-diffusion-mutation equation that we introduce to model the invasion of cane toads in Australia. This model is built off of one that has attracted…

We establish the logarithmic Bramson correction to the position of solutions to the Fisher--KPP equation with nonlocal diffusion. Solutions with step-like initial data typically resemble a front at position $c_{*} t - \frac{3}{2…

We study a variant of the Fisher-KPP equation with nonlocal dispersal. Using the theory of large deviations, we show the emergence of a "Bramson-like" logarithmic delay for the linearised equation with step-like initial data. We conclude…

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…

We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…

A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an…

The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the…

Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated…

We consider the solution to the scalar Fisher-KPP equation with front-like initial data, focusing on the location of its level sets at large times, particularly their deviation from points moving at the known spreading speed. We consider an…