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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 considered the problem of asymptotic decay as t \rightarrow + \infty $ of solutions of an abstract evolution equation of second order with a nonlinear and nonmonotone feedback.
Abstract: We consider the problem of asymptotic decay as t \rightarrow + \infty $ of solutions of an abstract evolution equation of second order with a nonlinear and nonmonotone feedback. Weak asymptotic stability of the global solutions is proved. This abstract result can be applied to different types of equations (wave, beam, and plate equations) and to different types of controls (interior, boundary, or pointwise controls). In particular, we significantly improve several earlier results on the asymptotic stability of the wave equation in a bounded domain with an interior or boundary control.

7 citations

Journal Article
TL;DR: In this article, alternative forms of asymptotic solutions of the Mathieu equation are derived with a view to generalizing the methods developed in a previous paper, so that these can then be applied to more complicated differential equations.
Abstract: Important alternative forms of asymptotic Solutions of the Mathieu equation are derived with a view to generalizing the methods developed in a previous paper, so that these can then be applied to more complicated differential equations. §

7 citations

Book ChapterDOI
A. Jeffrey1
01 Jan 1994
TL;DR: In this paper, the concepts of linear dispersive and dissipative wave propagation are reviewed, and then extended to travelling waves characterized by nonlinear evolution equations, and the general effect of nonlinearity on the development of a wave is examined and the propagation speed of a discontinuous solution (shock) is derived.
Abstract: In Section 1 the concepts of linear dispersive and dissipative wave propagation are reviewed, and then extended to travelling waves characterized by nonlinear evolution equations. The general effect of nonlinearity on the development of a wave is examined and the propagation speed of a discontinuous solution (shock) is derived. Various travelling wave solutions are discussed and soliton solutions of the KdV equation are mentioned. Section 2 reviews different ways of finding travelling wave solutions for the KdVB equation and comments on their equivalence. The ideas of weak and strong dispersion are then defined. The notion of a far field is introduced and hyperbolicity is discussed. Hyperbolic systems and waves form the topic of Section 3, which reviews Riemann invariants and simple waves, and their generalization. Shocks, the Riemann problem and entropy conditions are introduced. Sections 4 and 5 are concerned with the asymptotic derivation of far field equations both for systems and for scalar equations. The reductive perturbation method is described in Section 4 for weakly dispersive systems, while in Section 5 the multiple scale method is introduced and used to derive both the nonlinear Schrodinger and the KdV equation from a model nonlinear dispersive equation. Two physical examples with different evolution equations are given.

7 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered the asymptotic behavior with respect to time of the solution to the initial problem for an ordinary differential equation with a small parameter ∈ and constructed an approximation that is valid for time valuest≫∈ up to any order in ∈.
Abstract: We consider the asymptotic behavior with respect to time of the solution to the initial problem for an ordinary differential equation with a small parameter ∈. We construct an asymptotic approximation that is valid for time valuest≫∈ up to any order in ∈.

7 citations

Book ChapterDOI
01 Jan 1994
TL;DR: In this paper, the authors propose a simplification procedure for the electrical behavior of semiconductor devices in a nonlinear system of partial differential equations posed on domains with complicated geometries.
Abstract: In circuit simulation, device models should be as simple as possible. On the other hand, physically sound models for the electrical behaviour of semiconductor devices involve nonlinear systems of partial differential equations posed on domains with complicated geometries. Therefore simplifications have to be introduced corresponding to certain idealizing assumptions. By the use of asymptotic methods the simplification procedure can be carried out in a mathematically justifiable way.

7 citations


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