This work studies the expansion of the level sets of the solutions of a Fisher-KPP type reaction- diffusion equation, the diffusion being given by a nonnegative, compactly supported, even kernel. Because the latter is not assumed to be spherically symmetric, the level sets advance at an asymptotic speed given by a Freidlin-G\"artner type formula. The main contribution of this paper is to push the expansion up to terms that vanish as time goes to infinity, consisting in an asymptotically logarithmic delay corrected by an function that is constant in time, but depends on the direction of propagation.
This paper is concerned with the precise asymptotics, as time goes to infinity, of a transport problem in a half plane coupled with a nonlinear nonlocal boundary condition. This system arises from a class of models for the spatial spread of epdemics, its space independent version being the classical Kermack-McKendrick...
Grégory Faye, J. Roquejoffre, Ming-Min Zhang· 0 citations
We consider the one-dimensional random growth surface introduced by Adhikari and Chatterjee [AC24], where the height function is defined recursively via the heights at two neighboring sites and an independent noise term at each space-time point. In the subcritical regime, assuming uniformly bounded eighth moments of th...
Dang-Zheng Liu, Fang-Zhou Luo, Tian Wu et al.· 0 citations
We consider a McKean-Vlasov equation incorporating spatial fast oscillatory behavior into both the energetic and kinematic components of the model. The former is given in terms of a confining potential while the latter by an underlying metric. The equation is formulated as a gradient flow in the space of probability me...
In this work, we study the logistic equation with an indefinite weight and a nonlocal diffusion operator. We first apply local and global bifurcation results to establish the existence of positive solutions. Next, we use approximation methods to obtain solutions under weaker regularity assumptions on the terms of the e...
W. Cintra, Ismael Oliveira dos Anjos, J. R. Santos et al.· Journal of Fixed Point Theor...· 1 citation
The exponential decay of weak solutions towards the constant steady state of general cross-diffusion systems in bounded domains with no-flux boundary conditions is investigated. The proof of quantitative decay rates is based on the relative entropy method and involves two parameters: the exponent determining the entrop...
In this paper, we consider a free boundary problem with fractional diffusion $(-\Delta)^s$ $(0<s<1)$, as a model for species spreading, which can be viewed as a natural extension of the free boundary model in \cite{CDLL2019}, where the nonlocal diffusion term is defined via a continuous integrable kernel function $J(x)...
Hu-Yuan Chen, Yi-Hong Du, Wen-Jie Ni· 1 citation
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