Remarks on the energy decay for nonlinear wave equations with nonlinear localized dissipative terms

Mitsuhiro Nakao

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation with a nonlinear localized dissipation. To overcome a difficulty related to derivative-loss mechanism we employ a 'loan' method.

Original languageEnglish
Pages (from-to)2158-2169
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
Volume73
Issue number7
DOIs
Publication statusPublished - 2010 Oct 1
Externally publishedYes

Fingerprint

Energy Decay
Semilinear Wave Equation
Decay Estimates
Energy Estimates
Nonlinear Wave Equation
Wave equations
Initial-boundary-value Problem
Boundary value problems
Dissipation
Derivatives
Derivative
Term

Keywords

  • Energy decay
  • Localized dissipation
  • Nonlinear wave equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Remarks on the energy decay for nonlinear wave equations with nonlinear localized dissipative terms. / Nakao, Mitsuhiro.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 73, No. 7, 01.10.2010, p. 2158-2169.

Research output: Contribution to journalArticle

@article{760b69aa69d84fd585ad6d51cffdee23,
title = "Remarks on the energy decay for nonlinear wave equations with nonlinear localized dissipative terms",
abstract = "We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation with a nonlinear localized dissipation. To overcome a difficulty related to derivative-loss mechanism we employ a 'loan' method.",
keywords = "Energy decay, Localized dissipation, Nonlinear wave equation",
author = "Mitsuhiro Nakao",
year = "2010",
month = "10",
day = "1",
doi = "10.1016/j.na.2010.05.042",
language = "English",
volume = "73",
pages = "2158--2169",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Limited",
number = "7",

}

TY - JOUR

T1 - Remarks on the energy decay for nonlinear wave equations with nonlinear localized dissipative terms

AU - Nakao, Mitsuhiro

PY - 2010/10/1

Y1 - 2010/10/1

N2 - We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation with a nonlinear localized dissipation. To overcome a difficulty related to derivative-loss mechanism we employ a 'loan' method.

AB - We derive an energy decay estimate for solutions to the initial-boundary value problem of a semilinear wave equation with a nonlinear localized dissipation. To overcome a difficulty related to derivative-loss mechanism we employ a 'loan' method.

KW - Energy decay

KW - Localized dissipation

KW - Nonlinear wave equation

UR - http://www.scopus.com/inward/record.url?scp=77955430787&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955430787&partnerID=8YFLogxK

U2 - 10.1016/j.na.2010.05.042

DO - 10.1016/j.na.2010.05.042

M3 - Article

AN - SCOPUS:77955430787

VL - 73

SP - 2158

EP - 2169

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 7

ER -