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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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TL;DR: In this paper, Butuzov and Vasil'eva proposed an asymptotic theory for the free vibrations of an iced two-conductor bundled transmission line with a small parameter.
Abstract: Dynamical systems driven by small white noise: Asymptotic analysis and applications- to the paper by VF Butuzov and AB Vasil'eva- Singularly perturbed differential equations of parabolic type- Asymptotic methods in mathematical biology- to the paper by AS Bakaj- Integral manifolds and adiabatic invariants of systems in slow evolution- Asymptotic analysis of hamiltonian systems- Homogenization method for the study of composite media- Uniform asymptotic expresions for the fundamental matrix of singularly perturbed linear systems and applications- Slow/fast decoupling for linear boundary value problems- Numerical aspects of singular perturbation problems- The (Driven) Josephson equation: An exercise in asymptotics- Periodic solutions of the autonomous josephson equation- On the interaction of flames and sound- to the research papers- Application of a combined Galerkin-averaging method- Asymptotic expansions for singularly perturbed differential matrix riccati equations with applications to linear - Quadratic optimization problems- Singular perturbations of epidemic models involving a threshold- An asymptotic theory for the free vibrations of an iced two-conductor bundled transmission line- Linear methods in nonlinear problems with a small parameter- Relaxation oscillations including a standard chase on French ducks

3 citations

17 May 1988
TL;DR: In this paper, an asymptotic theory for a class of initial-boundary value problems for weakly nonlinear wave equations is presented, which implies the well-posedness of the problem in the classical sense and the validity of formal approximations on long time-scales.
Abstract: This chapter aims to contribute to the foundation of the asymptotic methods for initialboundary value problems and initial value problems for weakly nonlinear hyperbolic partial differential equations of order two. In this chapter an asymptotic theory for a class of initial-boundary value problems for weakly nonlinear wave equations is presented. The theory implies the well-posedness of the problem in the classical sense and the validity of formal approximations on long time-scales. As an application of the theory an initial-boundary value problem for a Rayleigh wave equation is studied in detail using a two-timescales perturbation method. From an aeroelastic analysis it is shown that this initial-boundary value problem may be regarded as a model describing the growth of wind-induced oscillations of overhead transmission lines.

3 citations

Journal ArticleDOI
TL;DR: In this article, the asymptotic properties of attainable sets of singularly-perturbed linear autonomous control systems are investigated and it is shown that if an explicitly given linear scaling operator is applied to the attainable set, the resulting sets converge (as the small parameter tends to zero).

3 citations

Journal ArticleDOI

3 citations

Journal ArticleDOI
TL;DR: A review of asymptotic methods in the theory of plates and shells can be found in this paper, where the authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.
Abstract: This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i) it is devoted to the fundamental principles of asymptotic approaches, and (ii) it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.

3 citations


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