Related papers: Asymptotic Spreading Fastened by Inter-Specific Co…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

We generalize the Mittag-Leffler function by attaching an exponent to its Taylor coefficients. The main result is an asymptotic formula valid in sectors of the complex plane, which extends work by Le Roy [Bull. des sciences math. 24, 1900]…

We determine the asymptotic spreading speed of an invasive species, which invades the territory of a native competitor, governed by a diffusive competition model with a free boundary in a spherically symmetric setting. This free boundary…

This paper presents a simple model for such processes as chaos spreading or turbulence spillover into stable regions. In this simple model the essential transport occurs via inelastic resonant interactions of waves on a lattice. The process…

We consider a class of cooperative reaction-diffusion systems with free boundaries in one space dimension, where the diffusion terms are nonlocal, given by integral operators involving suitable kernel functions, and they are allowed not to…

New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential…

We suggest a new method to compute the asymptotic fitness distribution in the Bak-Sneppen model of biological evolution. As applications we derive the full asymptotic distribution in the four-species model, and give an explicit linear…

Given a sequence of real rooted polynomials $\{p_n\}_{n\geq 1}$ with a fixed asymptotic root distribution, we study the asymptotic root distribution of the repeated polar derivatives of this sequence. This limiting distribution can be seen…

This paper is an introductory review of the problem of front propagation into unstable states. Our presentation is centered around the concept of the asymptotic linear spreading velocity v*, the asymptotic rate with which initially…

The paper is devoted to three-parametric self-similar Gaussian Volterra processes that generalize fractional Brownian motion. We study the asymptotic growth of such processes and the properties of long- and short-range dependence. Then we…

We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…

We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in…

We characterize the asymptotic speed of propagation of almost planar solutions to a semilinear viscous parabolic equation, with periodic nonlinearity.

For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…

We consider general models of coupled reaction-diffusion systems for interacting variants of the same species. When the total population becomes large with intensive competition, we prove that the frequencies (i.e. proportions) of the…

In this paper we study a nonlinear reaction-diffusion system which models an infectious disease caused by bacteria such as those for cholera. One of the significant features in this model is that a certain portion of the recovered human…

In this paper we focus on three problems about the spreading speeds of nonlocal dispersal Fisher-KPP equations. First, we study the signs of spreading speeds and find that they are determined by the asymmetry level of the nonlocal dispersal…

This paper is concerned with non-cooperative parabolic reaction--diffusion systems which share structural similarities with the scalar Fisher--KPP equation. In a previous paper, we established that these systems admit traveling wave…

Asymptotic couplings by reflection are constructed for a class of non-linear monotone SPDES (stochastic partial differential equations). As applications, the gradient/H\"older estimates as well as the exponential convergence are derived for…

In this paper, we study the asymptotic behavior of the solutions of nonlocal bistable reaction-diffusion equations starting from compactly supported initial conditions. Depending on the relationship between the nonlinearity, the interaction…