Matches in SemOpenAlex for { <https://semopenalex.org/work/W2046439822> ?p ?o ?g. }
Showing items 1 to 63 of
63
with 100 items per page.
- W2046439822 abstract "In this paper we study the method of aver- aging for functional differential equations and classes of par- tial differential equations when subjected to high frequency perturbations. 1. Introduction. It is a well-known fact that the motions described by systems modeled by ordinary differential equations (ODE) may change drastically when subjected to high frequency forcing functions. A classical example is the stabilization of a pendulum at the vertical position by rapidly oscillating the support. The amplitude of an undesirable limit cycle of an autonomous ODE may be decreased or the limit cycle even may be eliminated by such appropriately applied forces (see, for example, Andronov, Khaikin and Witt (2), Bogoliubov and Mitropolsky (5 )o r Hale (14) for these as well as other illustrations of similar phenomena). The appropriate tool for understanding the effects of high frequency input functions is the method of averaging. It is the purpose of this paper to give an extension of this method to infinite dimensional systems which will include some types of partial differential equations (PDE) as well as functional differential equations (FDE). We give a few illustrations of the method. Further applications to the control of mechanical systems can be found in a forthcoming paper of Lehman and Verduyn Lunel. To understand why new ideas are needed in our situation, it is worthwhile to present a brief summary of the method of averaging for ODE. Consider the system of ODE in R n , (1.1) ˙ x(t )= f (t/�, x ), whereis a small parameter and f (s, x )i s periodic ins of period one, the nonlinearity f (s, x) is continuous together with its derivative with respect to x. Our theory below will hold for f (s, x) which are almost periodic in s, but we present the ideas in the periodic case in order to avoid technical difficulties." @default.
- W2046439822 created "2016-06-24" @default.
- W2046439822 creator A5056303834 @default.
- W2046439822 creator A5061872406 @default.
- W2046439822 date "1990-12-01" @default.
- W2046439822 modified "2023-10-03" @default.
- W2046439822 title "Averaging in infinite dimensions" @default.
- W2046439822 cites W1481522385 @default.
- W2046439822 cites W1496528299 @default.
- W2046439822 cites W1560060148 @default.
- W2046439822 cites W1976166855 @default.
- W2046439822 cites W2003221488 @default.
- W2046439822 cites W2039775357 @default.
- W2046439822 cites W2055614104 @default.
- W2046439822 cites W2069419027 @default.
- W2046439822 cites W2108397312 @default.
- W2046439822 cites W2126178659 @default.
- W2046439822 cites W92209560 @default.
- W2046439822 doi "https://doi.org/10.1216/jiea/1181075583" @default.
- W2046439822 hasPublicationYear "1990" @default.
- W2046439822 type Work @default.
- W2046439822 sameAs 2046439822 @default.
- W2046439822 citedByCount "107" @default.
- W2046439822 countsByYear W20464398222012 @default.
- W2046439822 countsByYear W20464398222013 @default.
- W2046439822 countsByYear W20464398222015 @default.
- W2046439822 countsByYear W20464398222016 @default.
- W2046439822 countsByYear W20464398222017 @default.
- W2046439822 countsByYear W20464398222018 @default.
- W2046439822 countsByYear W20464398222019 @default.
- W2046439822 countsByYear W20464398222020 @default.
- W2046439822 countsByYear W20464398222021 @default.
- W2046439822 countsByYear W20464398222022 @default.
- W2046439822 countsByYear W20464398222023 @default.
- W2046439822 crossrefType "journal-article" @default.
- W2046439822 hasAuthorship W2046439822A5056303834 @default.
- W2046439822 hasAuthorship W2046439822A5061872406 @default.
- W2046439822 hasBestOaLocation W20464398221 @default.
- W2046439822 hasConcept C134306372 @default.
- W2046439822 hasConcept C202444582 @default.
- W2046439822 hasConcept C33923547 @default.
- W2046439822 hasConceptScore W2046439822C134306372 @default.
- W2046439822 hasConceptScore W2046439822C202444582 @default.
- W2046439822 hasConceptScore W2046439822C33923547 @default.
- W2046439822 hasIssue "4" @default.
- W2046439822 hasLocation W20464398221 @default.
- W2046439822 hasOpenAccess W2046439822 @default.
- W2046439822 hasPrimaryLocation W20464398221 @default.
- W2046439822 hasRelatedWork W1557945163 @default.
- W2046439822 hasRelatedWork W1985218657 @default.
- W2046439822 hasRelatedWork W2023661790 @default.
- W2046439822 hasRelatedWork W2064847051 @default.
- W2046439822 hasRelatedWork W2096753949 @default.
- W2046439822 hasRelatedWork W2742285599 @default.
- W2046439822 hasRelatedWork W2963341196 @default.
- W2046439822 hasRelatedWork W3103780039 @default.
- W2046439822 hasRelatedWork W3106133691 @default.
- W2046439822 hasRelatedWork W4249580765 @default.
- W2046439822 hasVolume "2" @default.
- W2046439822 isParatext "false" @default.
- W2046439822 isRetracted "false" @default.
- W2046439822 magId "2046439822" @default.
- W2046439822 workType "article" @default.