Almost periodic solutions of one dimensional wave equations with periodic coefficients
type: Item
instance of: scholarly article
title: Almost periodic solutions of one dimensional wave equations with periodic coefficients
zbMATH Open document ID: 0734.35003
author: Masaru Yamaguchi
published in: Journal of Mathematics of Kyoto University
publication date: 1989-01-01T00:00:00Z
review text: The author establishes conditions under which all solutions of an initial-boundary value problem for the equation \[ u_{xx}- u_{tt}+\epsilon (p(t)u+q(t)u_ t)=f(x,t),\quad x\in (0,\pi), \] are almost periodic, where \(\epsilon\) is a small parameter, p(t) and q(t) are periodic with period \(2\pi\) /\(\omega\) and f is almost periodic. The paper mainly deals with the case where the ratio \(2\pi\) /\(\omega\) is irrational and \(\int^{2\pi /\omega}_{0}q(t) dt=0\).
Mathematics Subject Classification ID: 35B15
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 4214458
reviewed by: Leonid Lebedev
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520221
OpenAlex ID: W1484290111
DOI: 10.1215/KJM/1250520221
Recommended article: Periodic solutions to one-dimensional wave equation with piece-wise constant coefficients
Recommended article: Periodic solutions for one dimensional wave equation with bounded nonlinearity
Recommended article: Q4317237
Recommended article: Almost-periodic solutions of an almost-periodically forced wave equation
Recommended article: Periodic solutions to one-dimensional wave equation with \(x\)-dependent coefficients
Recommended article: Q3847151
Recommended article: Periodic solutions to nonlinear one dimensional wave equation with 𝑋-dependent coefficients
Recommended article: Time-periodic solutions to the one-dimensional nonlinear wave equation
Recommended article: Q3793093
Recommended article: Periodic solutions of a quasilinear wave equation
description: scientific article; zbMATH DE number 4214458