Decay rates of energy of the 1D damped original nonlinear wave equation
type: Item
instance of: scholarly article
title: Decay rates of energy of the 1D damped original nonlinear wave equation
zbMATH Open document ID: 1481.35059
published in: Nonlinear Analysis. Real World Applications
publication date: 2021-12-15T00:00:00Z
review text: For one-dimension damped original nonlinear wave equations, the author constructed a new energy functional and considered its decay rate. Specifically speaking, he proved that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This fact can be used to recover the classical exponential, polynomial, or logarithmic decay rate for the linear, polynomial or exponentially degenerating damping force near the origin, respectively.
reviewed by: Dongbing Zha
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L72
Mathematics Subject Classification ID: 74K05
zbMATH DE Number: 7446125
zbMATH Keywords: energy function
zbMATH Keywords: nonlinear damping
zbMATH Keywords: perturbed energy method
zbMATH Keywords: generalized Young's inequality
author: Wei-Jiu Liu
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2021.103412
OpenAlex ID: W3196815539
cites work: A direct method for the boundary stabilization of the wave equation
cites work: Exact Controllability, Stabilization and Perturbations for Distributed Systems
cites work: The exponential stability of the problem of transmission of the wave equation
cites work: Stabilization and controllability for the transmission wave equation
cites work: Elementary feedback stabilization of the linear reaction-convection-diffusion equation and the wave equation
cites work: Q4282410
cites work: Decay estimates for some semilinear damped hyperbolic problems
cites work: Q4851730
cites work: Decay of solutions of wave equations in a bounded region with boundary dissipation
cites work: Stabilization of wave and plate-like equations with nonlinear dissipation on the boundary
cites work: Decay rates for dissipative wave equations
cites work: Asymptotic Behaviour of Solutions of the One-Dimensional Wave Equation with a Nonlinear Boundary Stabilizer
cites work: Uniform Stabilization of the Wave Equation by Nonlinear Boundary Feedback
cites work: Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
cites work: Energie decay estimates and exact boundary value controllability for the wave equation in a bounded domain
cites work: The rate at which energy decays in a damped String
cites work: Output-feedback stabilization of an unstable wave equation
cites work: Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions
cites work: Exponential decay for the semilinear wave equation with localized damping in unbounded domains
cites work: A new method to obtain decay rate estimates for dissipative systems with localized damping
cites work: Asymptotic stability of the bounded or almost periodic solution of the wave equation with nonlinear dissipative term
cites work: Energy decay for the wave equation with a nonlinear weak dissipation
cites work: Q4692311
cites work: \(L^p\)-asymptotic stability analysis of a 1D wave equation with a nonlinear damping
cites work: On the decay in \(W^{1,\infty}\) for the 1D semilinear damped wave equation on a bounded domain
cites work: One-dimensional wave equation with set-valued boundary damping: well-posedness, asymptotic stability, and decay rates
cites work: Q4094029
cites work: Introduction (to ``From finite to infinite dimensional dynamical systems'')
cites work: Q4073917
cites work: Asymptotic tracking and disturbance rejection of the blood glucose regulation system
cites work: Nonlinear Output Regulation
cites work: Boundary feedforward and feedback control for the exponential tracking of the unstable high-dimensional wave equation
cites work: Independence of convergence rate of the wave tracking error on structures of feedforward controllers
cites work: Feedforward Boundary Control for the Regulation of a Passive and Diffusive Scalar in Two-Dimensional Unsteady Flows
cites work: The State Feedback Regulator Problem for Regular Linear Systems
DOI: 10.1016/J.NONRWA.2021.103412
description: scientific article; zbMATH DE number 7446125