Asymptotic Analysis - Volume 96, issue 1

Authors: Gurevich, Pavel | Rachinskii, Dmitrii

Article Type: Research Article

Abstract: We consider a reaction–diffusion system including discontinuous hysteretic relay operators in reaction terms. This system is motivated by an epigenetic model that describes the evolution of a population of organisms which can switch their phenotype in response to changes of the state of the environment. The model exhibits formation of patterns in the space of distributions of the phenotypes over the range of admissible switching strategies. We propose asymptotic formulas for the pattern and the process of its formation.

Keywords: reaction–diffusion equations, patterns, phenotype switching, hysteresis, free boundary, asymptotic limit of slow diffusion

DOI: 10.3233/ASY-151329

Citation: Asymptotic Analysis, vol. 96, no. 1, pp. 1-22, 2016

Authors: Cavazos-Cadena, Rolando | Hernández-Hernández, Daniel

Article Type: Research Article

Abstract: This work concerns Markov chains evolving on a denumerable sate space, which is endowed with a non-negative reward function with finite support. In this context, the problem of determining the Varadhan function, given by the exponential growth rate of the aggregated rewards, is studied. The main results in this direction are expressed in terms of the idea of a  system of local Poisson equations , and can be summarized as follows: (i) the Varadhan function is determined by one of such systems, and (ii) if a finite set is accessible form any state, then a system of local Poisson equations exits.

Keywords: discounted approximation, fixed points, stopping time, accessibility to a finite set, weak Doeblin condition, risk-sensitive average reward

DOI: 10.3233/ASY-151331

Citation: Asymptotic Analysis, vol. 96, no. 1, pp. 23-50, 2016

Authors: Huneau, Cécile

Article Type: Research Article

Abstract: We solve the Einstein constraint equations for a ( 3 + 1 ) -dimensional vacuum space–time with a space-like translational Killing field in the asymptotically flat case. The presence of a space-like translational Killing field allows for a reduction of the ( 3 + 1 ) -dimensional problem to a ( 2 + 1 ) -dimensional one. The aim of this paper is to go further in the asymptotic expansion of the solutions than in [Constraint equations for 3 + 1 vacuum Einstein equations with a translational space-like Killing field in …the asymptotically flat case, available at: arXiv:1302.1473 ]. In particular the expansion we construct involves quantities which are the 2-dimensional equivalent of the global charges. Show more

Keywords: general relativity, Einstein constraint equations, asymptotic flatness

DOI: 10.3233/ASY-151333

Citation: Asymptotic Analysis, vol. 96, no. 1, pp. 51-89, 2016