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Showing papers on "Asymptotology published in 1995"


Book ChapterDOI
01 Jan 1995

303 citations




Book
01 Jan 1995
TL;DR: This paper presents an asymptotic approximation of the Navier-Stokes model for small and large mean free path and some models of this approximation are compared to the Boltzmann model.
Abstract: Preface The basics of asymptotics Perturbation theory Model examples Models of asymptotic approximation of the Navier-Stokes model Asymptotic approximation of the Boltzmann model for small and large mean free path Other models of asymptotic approximation References Index

24 citations


Journal ArticleDOI
Manuel Pinto1
TL;DR: In this article, a number of results on asymptotic equivalence of bounded and unbounded solutions of difference systems were obtained using h- systems and (h, k)- dichotomies.
Abstract: Using h- systems and (h, k)- dichotomies we obtain a number of results on asymptotic equivalence of bounded and unbounded solutions of difference systems.

11 citations


Journal ArticleDOI
TL;DR: In this article, an application of the asymptotic method of nonlinear mechanics to the construction of an approximate solution of the Klein-Gordon equation was considered, and the authors considered an application to nonlinear nonlinear problems.
Abstract: We consider an application of the asymptotic method of nonlinear mechanics to the construction of an approximate solution of the Klein-Gordon equation.

9 citations





Journal ArticleDOI
TL;DR: In this paper, the authors generalize LeCam's third lemma by using the rate of convergence in the case of asymptotically efficient test statistics, which is specified to linear combinations of order statistics and linear rank statistics.
Abstract: Asymptotic distributions of test statistics under alternatives are important from the point of view of their power properties. When the limiting distributions of test statistics are specified under the hypothesis in a certain sense, LeCam's third lemma ([4], Chapter 6) enables one to obtain their limiting distributions under close alternatives. In this paper we generalize LeCam's third lemma by using the rate of convergence in the case of asymptotically efficient test statistics. A general lemma is proved which is specified to linear combinations of order statistics (L-statistics) and linear rank statistics (R-statistics). Edgeworth-type asymptotic expansions for these statistics under alternatives are considered in [3].

6 citations


Journal ArticleDOI
TL;DR: In this paper, the authors considered a dynamic system of 2-D nonlinear elasticity with nonlinear interior dissipation and showed that in the case of zero load applied to the plate, the arbitrarily large decay rates can be achieved provided that both the damping coefficient and the extraction coefficient are sufficiently large.
Abstract: A Dynamic system of 2-D nonlinear elasticity with nonlinear interior dissipation is considered. It is assumed that the principal part of elastic operator is perturbed by the unstructured lower order linear terms. Asymptotic behavior of solutions when time $t \rightarrow 0$ is analyzed. It is shown that in the case of zero load applied to the plate, the arbitrarily large decay rates can be achieved provided that both the "damping" coefficient and the "traction" coefficient are suitably large. This result generalizes and extends, to the nonlinear and multidimensional context, the earlier results obtained only for the one-dimensional linear wave equation. In the case of a loaded plate the existence of compact global attractor attracting all solutions is established.


Journal ArticleDOI
TL;DR: For a simple model of a linear kinetic equation, the exact solution is expanded in terms of a small parameter whose presence makes the equation, singularly perturbed as discussed by the authors, and it is shown that the compressed method, which is related to the Chapman-Enskog asymptotic procedure, is the most accurate.
Abstract: For a simple model of a linear kinetic equation the exact solution is expanded in terms of a small parameter whose presence makes the equation, singularly perturbed. Various asymptotic expansion methods are analyzed and it is shown that the compressed method, which is related to the Chapman-Enskog asymptotic procedure, is the most accurate. This holds when the technique of time rescaling is applied to overcome the difficulties with the application of the standard asymptotic procedure.

Book ChapterDOI
01 Jan 1995
TL;DR: In this article, a generalization of Levy walk in one dimension allowing for an arbitrary bias and asymmetry of jumps is proposed, where an asymptotic distribution of distance R(t) reached up to time t by a particle initially at the origin is found to be a possibly asymmetric Levy-stable law s α,β (τ) or a positive law hλ(xx).
Abstract: We propose a generalization of Levy walk in one dimension allowing for an arbitrary bias and asymmetry of jumps. An asymptotic distribution (propagator) of distance R(t) reached up to time t by a particle initially at the origin is found to be a possibly asymmetric Levy-stable law s α,β (τ) or a positive law hλ(xx). A probabilistic approach in terms of random variables R; and T i is applied.

Journal ArticleDOI
TL;DR: In this paper, a framework for the analysis of uniform asymptotic stability of nonlinear systems with continuous motions is presented, which relies on the very foundations of the Lyapunov stability concept and the second-order method.
Abstract: The framework of the presented research is a large class of time-varying nonlinear systems with continuous motions. The study of the uniform asymptotic stability of the zero equilibrium state developed here goes back to, and relies on, the very foundations of the Lyapunov stability concept and the (second) Lyapunov method. Stability domains are first defined and examined. Then, their qualitative features are used to establish complete solutions to the problem of uniform asymptotic stability of the equilibrium for various subclasses of the systems. The solutions present conditions that are both necessary and sufficient for: (1) the uniform asymptotic stability, (2) an exact direct one-shot construction of a system Lyapunov function and (3) for a direct accurate one-shot determination of the asymptotic stability domain. In addition, the solutions establish a novel Lyapunov-method based approach to the asymptotic stability analysis. This enables an arbitrary selection of a function p(·) from a defined functi...

Journal ArticleDOI
TL;DR: In this paper, one-frequency approximations of asymptotic solutions by using periodic Ateb-functions were constructed for a non-autonomous wave equation with homogeneous boundary conditions.
Abstract: For a nonautonomous wave equation with homogeneous boundary conditions, we construct one-frequency approximations of asymptotic solutions by using periodic Ateb-functions. Resonance and nonresonance cases are considered.

Journal ArticleDOI
TL;DR: In this article, an asymptotic approximation is applied to study the instability of slow hydromagnetic waves with magnetic diffusion, where the waves are short in some directions other than the azimuthal, and vary slowly in those directions.

Book ChapterDOI
01 Jan 1995
TL;DR: In this paper, the continuity in norm of the resolvent in the parameter plays the fundamental role in analytic or uniform perturbation theory, and it is shown that under suitable conditions, the possibility of asymptotic expansions of these quantities can be deduced.
Abstract: In the foregoing chapters we have been concerned almost exclusively with analytic or uniform perturbation theory, in which the continuity in norm of the resolvent in the parameter plays the fundamental role. We shall now go into a study in which the basic notion is the strong continuity of the resolvent. Here the assumptions are weakened to such an extent that the analyticity of the resolvent or of the eigenvalues of the operator as functions of the parameter cannot be concluded, but we shall be able to deduce, under suitable conditions, the possibility of asymptotic expansions of these quantities.

Journal ArticleDOI
Boling Guo1, Shaobin Tan1
TL;DR: In this article, the authors studied the long time asymptotic behavior of nonlinear Schrodinger equations with magnetic effect and proved the existence and nonexistence of the non-trivial free solutions.
Abstract: The purpose of this paper is to study the long time asymptotic behavior for a nonlinear Schrodinger equations with magnetic effect. Under certain conditions, we prove the existence and nonexistence of the non-trivial free asymptotic solutions. In addition, the decay estimates of the solutions are also obtained.

Journal ArticleDOI
TL;DR: In this article, three lemmas are provided for additive correlation involving the Asymptotic Linearity Theorems, which were constructed for a study of the correlation between structure and properties in molecules having many identical moieties.
Abstract: The present article provides three lemmas that initiate the generalization of the theory of additive correlation involving the Asymptotic Linearity Theorems, which were constructed for a study of the correlation between structure and properties in molecules having many identical moieties. The new tools provided here also help to pave the way to linking the above theory with a theoretical framework developed for the asymptotic analysis of certain chemical kinetic network systems.

Journal ArticleDOI
TL;DR: In this paper, asymptotic parametric estimation from a particle process of birth and death on a Brownian flow is considered. And when that law is specifically that of a Poisson random measure, the authors treat a computational formula for asymPTI including Fisher's information for the maximum-likelihood estimator.


Journal ArticleDOI
TL;DR: In this paper, it was shown that Jorgens' asymptotic expansion theorem holds under the maximum norm. But the assumption that all the cross sections are continuous was not considered.
Abstract: This paper is devoted to discussing neutron transport system in a finite convex body with continuous energy bounded away from the origin. Under the assumptions that all the cross sections are continuous, it is shown, by virtue of the integrated semigroup theory, that Jorgens`s asymptotic expansion theorem hold under the maximum norm. 24 refs.


Journal ArticleDOI
T. Sasagawa1
TL;DR: In this article, the behavior of a system is deeply related to asymptotic properties of functions describing the system, and the properties of a function describing a system involve subtle points from the mathematical point of view.




Journal ArticleDOI
TL;DR: In this paper, the authors studied the asymptotic behavior of the fundamental solution of the Cauchy problem for the parabolic equation, where the coefficient can be written as in the form, where the function has an asymptic expansion as in positive powers of and.
Abstract: We study the asymptotic behaviour as of the fundamental solution (FS) of the Cauchy problem for the parabolic equation , , . We suppose that the coefficient can be written as in the form , where the function has an asymptotic expansion as in positive powers of and . We construct and justify the asymptotic expansion of the FS as up to any power of for the whole plane .

Posted Content
17 Apr 1995
TL;DR: In this paper, a new approach to the problem of finding the asymptotical behavior of large orders of semiclassical expansion is suggested, which can apply not only functional integral technique, which has been used up to now, but also method of direct analysis of the recursive relations.
Abstract: A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can apply not only functional integral technique, which has been used up to now, but also method of direct analysis of the semiclassical expansion recursive relations.