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The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand.
Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
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
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