Decay of solutions of the wave equation with a local nonlinear dissipation
type: Item
instance of: scholarly article
title: Decay of solutions of the wave equation with a local nonlinear dissipation
zbMATH Open document ID: 0856.35084
DOI: 10.1007/BF01444231
author: Mitsuhiro Nakao
published in: Mathematische Annalen
publication date: 1996-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/182997
review text: We derive precise decay estimates of the energy for the solutions to the initial-boundary value problem for the wave equation with a nonlinear dissipative term \[ u_{tt}- \Delta u+ \rho(x, u_t)= 0\quad \text{in } \Omega\times [0, \infty) \] with the boundary condition \(u|_{\partial\Omega}= 0\), where \(\rho(x, v)\) is a function like \(\rho(x, v)= a(x)|v|^r v\), \(- 1< r\), with \(a(x)\) supported only on a neighbourhood of some part of the boundary \(\partial\Omega\).
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 931967
zbMATH Keywords: decay estimates of the energy
zbMATH Keywords: nonlinear dissipative term
MaRDI profile type: Publication
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OpenAlex ID: W2026523808
description: scientific article; zbMATH DE number 931967