On the energy estimates of the wave equation with time dependent propagation speed asymptotically monotone functions
type: Item
instance of: scholarly article
title: On the energy estimates of the wave equation with time dependent propagation speed asymptotically monotone functions
zbMATH Open document ID: 1330.35050
author: M. R. Ebert
author: Laila Fitriana
author: Fumihiko Hirosawa
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-09-04T00:00:00Z
review text: A Cauchy problem for the wave equation with time dependent propagation speed is investigated. Denote \(a(t)\) the propagation speed and \(E(t)\) the total energy defined as the sum of the elastic and kinetic energy. Under some special assumptions on the propagation speed \(a(t)\) and initial data, one proves lower and upper bounds for the energy \(E(t)\), in terms of \(E(0)\). There is a large discussion around the validity of different generalized energy conservation type inequalities, the GECs, as well as the energy estimates.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 6478611
zbMATH Keywords: lower and upper bounds for the energy
MaRDI profile type: Publication
full work available at URL: j.jmaa.2015.06.051
OpenAlex ID: W2202652987
cites work: On the Gevrey well-posedness for second order strictly hyperbolic Cauchy problems under the influence of the regularity of the coefficients
cites work: Energy estimates at infinity for hyperbolic equations with oscillating coefficients
cites work: Q5699168
cites work: Q3207471
cites work: Q3331627
cites work: Energy decay for a degenerate hyperbolic equation with a dissipative term
cites work: On the asymptotic behavior of the energy for the wave equations with time depending coefficients
cites work: On second order weakly hyperbolic equations with oscillating coefficients and regularity loss of the solutions
cites work: Energy estimates for wave equations with time dependent propagation speeds in the Gevrey class
cites work: On the Global Solvability for Semilinear Wave Equations with Smooth Time Dependent Propagation Speeds
cites work: On second order weakly hyperbolic equations and the ultradifferentiable classes
cites work: Generalised energy conservation law for wave equations with variable propagation speed
cites work: \(L^p\)-\(L^q\) estimate for wave equation with bounded time dependent coefficient
cites work: Q4488141
cites work: Q4274290
cites work: Q5703552
cites work: Unique existence of evolution equations of hyperbolic type with countably many singular or degenerate points
DOI: 10.1016/J.JMAA.2015.06.051
description: scientific article; zbMATH DE number 6478611