Super-linear spreading in local and non-local cane toads equations

Super-linear spreading in local bistable cane toads equations

In this paper, we study the influence of an Allee effect on the spreading rate in a local reaction-diffusion-mutation equation modeling the invasion of cane toads in Australia. We are, in particular, concerned with the case when the diffusivity can take unbounded values. We show that the acceleration feature that arises in this model with a Fisher-KPP, or monostable, non-linearity still occurs ...

Super-linear spreading in local and non-local cane toads equations

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 toads is structured by a phenotypical trait that governs the spatial diffusion. In this paper, we are concerned with the case when the diffusivity can take ...

The Bramson logarithmic delay in the cane toads equations

We study a nonlocal reaction-diffusion-mutation equation modeling the spreading of a cane toads population structured by a phenotypical trait responsible for the spatial diffusion rate. When the trait space is bounded, the cane toads equation admits traveling wave solutions [7]. Here, we prove a Bramson type spreading result: the lag between the position of solutions with localized initial data...

Linear Diophantine Equations and Local Cohomology

What can be said about the set E ~ of solutions in nonnegative integers to a system of linear equations with integer coefficients? For many purposes, such as those of linear programming, this question has been adequately answered. However, when this question is regarded from the vantage point of commutative algebra, many additional aspects arise. In particular, there is a natural way to associa...

Fuzzy Local Fractional Differential Equations