Global existence for semilinear wave equations in exterior domains

M. Nakao

Research output: Contribution to journalArticle

Abstract

We consider exterior problems for linear and semilinear wave equations. We first derive total energy decay for the linear wave equation with a localized dissipation which is effective near infinity and critical part of the boundary. This can be applied to the proof of the global existence of finite energy or H2 solutions for semilinear wave equations. Next, by use of the local energy decay: we show Lp estimates for the linear equations with a dissipation effective only near a part of the boundary and apply this again to the global existence of semilinear equations.

Original languageEnglish
Pages (from-to)2497-2506
Number of pages10
JournalNonlinear Analysis, Theory, Methods and Applications
Volume47
Issue number4
DOIs
Publication statusPublished - 2001 Aug
Externally publishedYes

Fingerprint

Semilinear Wave Equation
Exterior Domain
Wave equations
Global Existence
Dissipation
Linear equation
Local Energy Decay
Lp Estimates
Energy Decay
Exterior Problem
Semilinear Equations
Wave equation
Infinity
Linear equations
Energy

Keywords

  • Energy decay
  • Global existence
  • L estimates
  • Semilinear wave equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Global existence for semilinear wave equations in exterior domains. / Nakao, M.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 47, No. 4, 08.2001, p. 2497-2506.

Research output: Contribution to journalArticle

@article{5593ecd6c6f94aa8a5cafb95b04ba341,
title = "Global existence for semilinear wave equations in exterior domains",
abstract = "We consider exterior problems for linear and semilinear wave equations. We first derive total energy decay for the linear wave equation with a localized dissipation which is effective near infinity and critical part of the boundary. This can be applied to the proof of the global existence of finite energy or H2 solutions for semilinear wave equations. Next, by use of the local energy decay: we show Lp estimates for the linear equations with a dissipation effective only near a part of the boundary and apply this again to the global existence of semilinear equations.",
keywords = "Energy decay, Global existence, L estimates, Semilinear wave equations",
author = "M. Nakao",
year = "2001",
month = "8",
doi = "10.1016/S0362-546X(01)00372-8",
language = "English",
volume = "47",
pages = "2497--2506",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Limited",
number = "4",

}

TY - JOUR

T1 - Global existence for semilinear wave equations in exterior domains

AU - Nakao, M.

PY - 2001/8

Y1 - 2001/8

N2 - We consider exterior problems for linear and semilinear wave equations. We first derive total energy decay for the linear wave equation with a localized dissipation which is effective near infinity and critical part of the boundary. This can be applied to the proof of the global existence of finite energy or H2 solutions for semilinear wave equations. Next, by use of the local energy decay: we show Lp estimates for the linear equations with a dissipation effective only near a part of the boundary and apply this again to the global existence of semilinear equations.

AB - We consider exterior problems for linear and semilinear wave equations. We first derive total energy decay for the linear wave equation with a localized dissipation which is effective near infinity and critical part of the boundary. This can be applied to the proof of the global existence of finite energy or H2 solutions for semilinear wave equations. Next, by use of the local energy decay: we show Lp estimates for the linear equations with a dissipation effective only near a part of the boundary and apply this again to the global existence of semilinear equations.

KW - Energy decay

KW - Global existence

KW - L estimates

KW - Semilinear wave equations

UR - http://www.scopus.com/inward/record.url?scp=0035421848&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035421848&partnerID=8YFLogxK

U2 - 10.1016/S0362-546X(01)00372-8

DO - 10.1016/S0362-546X(01)00372-8

M3 - Article

AN - SCOPUS:0035421848

VL - 47

SP - 2497

EP - 2506

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 4

ER -