A pointwise oscillation property of semilinear wave equations with time-dependent coefficients
type: Item
instance of: scholarly article
title: A pointwise oscillation property of semilinear wave equations with time-dependent coefficients
zbMATH Open document ID: 1026.35008
DOI: 10.1016/S0362-546X(03)00159-7
author: Hiroshi Uesaka
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-09-07T00:00:00Z
review text: Under some assumptions on coefficients the author proves: If a solution \(u(x,t)\) to the equation \((a(t)u_t)_t-b(t)u_{xx}+c(t)u_t+d(t)u+f(t,u)=0, t>0,x\in (0,l)\) satisfying homogeneous boundary conditions does not identically vanish, then it oscillates, i.e. for any fixed \(x\), \(u(x,t)\) changes its sign infinitely many times on an infinite \(t\)-interval.
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 1975866
zbMATH Keywords: Dirichlet boundary condition
zbMATH Keywords: Neumann boundary condition
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
cites work: Q4748596
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cites work: Oscillation theory
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cites work: Oscillatory behavior of solutions of nonlinear wave equations
description: scientific article; zbMATH DE number 1975866