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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: In this article, the authors investigated the large-time asymptotic behavior of solutions of the Cauchy problem for a non-linear Sobolev-type equation with dissipation.
Abstract: The large-time asymptotic behaviour of solutions of the Cauchy problem is investigated for a non-linear Sobolev-type equation with dissipation. For small initial data the approach taken is based on a detailed analysis of the Green's function of the linear problem and the use of the contraction mapping method. The case of large initial data is also closely considered. In the supercritical case the asymptotic formulae are quasi-linear. The asymptotic behaviour of solutions of a non-linear Sobolev-type equation with a critical non-linearity of the non-convective kind differs by a logarithmic correction term from the behaviour of solutions of the corresponding linear equation. For a critical convective non-linearity, as well as for a subcritical non-convective non-linearity it is proved that the leading term of the asymptotic expression for large times is a self-similar solution. For Sobolev equations with convective non-linearity the asymptotic behaviour of solutions in the subcritical case is the product of a rarefaction wave and a shock wave. Bibliography: 84 titles.

4 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied uniform approximation of functions in a fixed subset of OFnOD by functions holomorphic in D. The method of proof will depend on the results in [10] where the special case E = 8FnSD is studied.
Abstract: If h exists whenever f and e are given, F is called a set of uniform approximation for H(D). Arakelian [1] has given a complete geometrical description of these sets: \"F is a set of uniform approximation for H(D) if and only if D*\\ F is connected and locally connected, where D* denotes the one point compactification of D\". If E is a fixed subset of OFnOD, let A~F) denote all continuous functions f on FuE such that flee A(F). (We assume F carries the induced spherical metric.) In § 1 we study uniform approximation of functions in AE(F) by functions holomorphic in D. The sets of uniform approximation are given a geometrical description which coinsides with Arakelians if E is empty. The method of proof will depend on the results in [10] where the special case E= 8FnSD is studied. Consider now a set F which is a set of uniform approximation for H(D). Given f and e we can then seek a better approximant hlEH(D ) such that If(z)-hl(z)l

4 citations

Book
01 Dec 1998
TL;DR: The notion of asymptotic convergence was introduced in this paper for solving multidimensional inverse gravimetry problems on the basis of an iterative method for solution of the problem.
Abstract: Part 1 The notion of asymptotic convergence. Part 2 Asymptotic models for equations of mathematical physics: asymptotic the Helmholtz equation asymptotic models for the equation of the contact gravimetry problem asymptotic models for equations of geometric optics asymptotic models for Maxwell equation system the dual asymptotic models for the elliptic system the dual asymptotic models for the Maxwell equation system. Part 3 The iterative methods for solution of multidimensional inverse problems on the basis of the asymptotic models: on quasi-solution uniqueness of operator equations asymptotic approximation to the inverse problem solution for the Helmholtz equation conditions for applications of the iterative asymptotic method for solution of multidimensional problems the asymptotic method for solution of the inverse gravimetry problem (Part contents).

4 citations

Journal ArticleDOI
TL;DR: The concordance method of asymptotic expansions applied for constructing uniform expansion of singularly-perturbed partial differential equations and systems is presented in this paper, where the concordances are applied to construct uniform expansion.
Abstract: The concordance method of asymptotic expansions applied for constructing uniform asymptotic expansions of singularly-perturbed partial differential equations and systems is presented.

4 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the connection between the asymptotic and quasi-asymptotic properties at infinity of slowly increasing generalized functions with supports on the half-line and the real parts of their Laplace and Fourier transforms in a neighborhood of the origin.
Abstract: This paper studies the connection between the asymptotic and quasi-asymptotic properties at infinity of slowly increasing generalized functions with supports on the half-line and the asymptotic and quasi-asymptotic properties of the real parts of their Laplace and Fourier transforms in a neighborhood of the origin. The study is caried out in the scale of regularly varying self-similar functions. The results are applied to the study of the asymptotic properties of solutions of linear passive systems, and also to the study of the connection between Abel and Ces?ro convergence (with respect to a self-similar weight) of the Fourier-Stieltjes series of nonnegative measures. Bibliography: 13 titles.

4 citations


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