Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
Papers published on a yearly basis
Papers
More filters
••
21 citations
••
TL;DR: Following Kasminski, this paper investigated the asymptotic behavior of solutions of linear time-independent Ito equations and gave a sufficient condition for stability of the zero solution in dimension 2.
Abstract: Following Kasminski, we investigate asymptotic behavior of solutions of linear time-independent Ito equations We first give a sufficient condition for asymptotic stability of the zero solution Then in dimension 2 we determine conditions for spiraling at a linear rate Finally we give applications to the Cauchy problem for the associated parabolic equation by the use of a tauberian theorem Introduction Consider a system of linear, constant coefficients differential equations dx I (0 1) -d=Ebxj x (I 01, he gave a necessary and sufficient condition that r(t) 0 as when t --> He did not examine, however, the behavior of {X(t), t > 01 The first study of the angular behavior in the case 1 2 Received by the editors March 13, 1972, AMS (MOS) subject classifications (1970) Primary 60H10, 60J60; Secondary 34D05, 34A30, 34C05
21 citations
••
21 citations
••
TL;DR: A Chapman-Enskog-type asymptotic expansion is introduced and an effective system of equations describing the late-time/stiff relaxation singular limit is derived, and a new finite volume discretization is proposed which allows for a discrete version of the same effective asymPTotic system.
Abstract: We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-Enskog-type asymptotic expansion and derive an effective system of equations describing the late-time/stiff relaxation singular limit. The structure of this new system is discussed and the role of a mathematical entropy is emphasized. Second, we propose a new finite volume discretization which, in late-time asymptotics, allows us to recover a discrete version of the same effective asymptotic system. This is achieved provided we suitably discretize the relaxation term in a way that depends on a matrix-valued free-parameter, chosen so that the desired asymptotic behavior is obtained. Our results are illustrated with several models of interest in continuum physics, and numerical experiments demonstrate the relevance of the proposed theory and numerical strategy.
21 citations