Asymptotic expansions of a boundary-value problem for a certain nonlinear partial differential equation
type: Item
instance of: scholarly article
title: Asymptotic expansions of a boundary-value problem for a certain nonlinear partial differential equation
zbMATH Open document ID: 0541.35052
DOI: 10.1007/BF01093588
author: B. I. Sokil
published in: Ukrainian Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: Consider the nonlinear, nonhomogeneous equation \[ \partial^ 2u/\partial t^ 2-\alpha(\partial u/\partial x)^ n\partial^ 2u/\partial x^ 2=\epsilon f(x,u,\partial u/\partial x,\partial u/\partial t,\partial^ 2u/\partial x^ 2,\nu t) \] where \(\alpha>0\), \(n+1=(2m+1)/(2r+1), m,r=0,1,...,t>0\), \(\epsilon\) a small parameter, \(f(x,u,\partial u/\partial x,\partial u/\partial t,\partial^ 2u/\partial x^ 2,\nu t)\) an analytic 2\(\pi\)-periodic (with respect to \(\nu\) t) function. Using special Ateb functions [see \textit{P. M. Senik}, Ukr. Mat. Zh. 21, 325-333 (1969; Zbl 0201.069)] the author constructs in a ''nonresonance'' case one- frequency asymptotic solutions of the above equation.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 3859620
zbMATH Keywords: wave propagation
zbMATH Keywords: nonlinear
zbMATH Keywords: nonhomogeneous
zbMATH Keywords: nonresonance
zbMATH Keywords: one-frequency asymptotic solutions
Wikidata QID: Q115394127
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3859620