Applications of the asymptotic method to the investigation of a hyperbolic impulsive system
type: Item
instance of: scholarly article
title: Applications of the asymptotic method to the investigation of a hyperbolic impulsive system
zbMATH Open document ID: 0681.35059
DOI: 10.1007/BF01056481
published in: Ukrainian Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: The author constructs an asymptotic approximation for the periodic solutions of the hyperbolic equation \[ u_{tt}-c^ 2u_{xx}+\lambda^ 2u=\epsilon f(u,u_ t,u_ x) \] with impulse input in the time \(t_ 0\) given by \[ u_ t(t_ 0+0,x)-u_ t(t_ 0- 0,x)=\epsilon I(u_ t(t_ 0-0,x)). \] Here \(\epsilon\) is a small parameter and f and I are sufficiently smooth functions.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 4115147
zbMATH Keywords: asymptotic approximation
zbMATH Keywords: periodic solutions
zbMATH Keywords: impulse input
author: Svitlana P. Rogovchenko
MaRDI profile type: Publication
cites work: Q4746878
cites work: Q5682682
cites work: Secular and Nonsecular Behavior for the Cold Plasma Equations
full work available at URL: https://doi.org/10.1007/bf01056481
OpenAlex ID: W2078351346
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description: scientific article; zbMATH DE number 4115147