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Asymptotology

About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.


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Journal ArticleDOI
TL;DR: An analysis of the non-Hermitian fluid systems described by the Rayleigh equation in an unbounded domain has been carried out in the regime of large wave numbers and it is shown that the divergent expansion is renormalizable by means of the renormalization group method-the renormalized results are in complete conformity with the asymptotic solutions.
Abstract: An analysis of the non-Hermitian fluid systems described by the Rayleigh equation in an unbounded domain has been carried out in the regime of large wave numbers. The evolution of a special class of localized vorticities is also discussed. Asymptotic and perturbative approaches lead to the same final result. In the limit considered, the system is stable. The perturbation analysis reveals interesting pathologies of the non-Hermitian systems. Under specific conditions, the expansion is found to show secular growth. A discussion about the mechanism of insurgence of such singular behavior is presented. It is also shown that the divergent expansion is renormalizable by means of the renormalization group method---the renormalized results are in complete conformity with the asymptotic solutions.

6 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered the fourth Painleve equation with nonzero values of its two complex parameters a and b and obtained nine families of power asymptotic forms extended by asymythmic expansions.
Abstract: We consider the fourth Painleve equation with nonzero values of its two complex parameters a and b . Asymptotic forms of power, complicated, exotic, and elliptic types for its solutions near the points x = 0 and x = ∞ are sought by methods of two- and three-dimensional power geometry. We obtain nine families of power asymptotic forms extended by asymptotic expansions and one family of elliptic asymptotic forms. Complicated and exotic asymptotic forms are absent.

6 citations

01 Jan 2002
TL;DR: In this article, the generalized Epstein-Hubbell integral is considered for values of the variable k close to its upper limit k = 1, and the distributional approach is used for deriving two convergent expansions of this integral in increasing powers of 1 - k 2.
Abstract: The generalized Epstein-Hubbell integral recently introduced by Kalla & Tuan (Comput. Math. Applic. 32,1996) is considered for values of the variable k close to its upper limit k = 1. Distributional approach is used for deriving two convergent expansions of this integral in increasing powers of 1 - k 2 . For certain values of the parameters, one of these expansions involves also a logarithmic term in the asymptotic variable 1 - k 2 . Coefficients of these expansions are given in terms of the Appell function and its derivative. All the expansions are accompanied by an error bound at any order of the approximation. Numerical experiments show that this bound is considerably accurate.

6 citations

01 Jan 1974

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.

6 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526