Decay estimates of solutions to wave equations in conical sets

Michael Dreher

Research output: Contribution to journalArticle

Abstract

We consider the wave equation in an unbounded conical domain, with initial conditions and boundary conditions of Dirichlet or Neumann type. We give a uniform decay estimate of the solution in terms of weighted Sobolev norms of the initial data. The decay rate is the same as in the full space case.

Original languageEnglish
Pages (from-to)477-501
Number of pages25
JournalCommunications in Partial Differential Equations
Volume32
Issue number3
DOIs
Publication statusPublished - 2007

Keywords

  • decay estimates
  • fractional integrals
  • representation of solution
  • LINEAR EVOLUTION-EQUATIONS
  • SMALL AMPLITUDE SOLUTIONS
  • NONLINEAR HYPERBOLIC-EQUATIONS
  • KLEIN-GORDON EQUATIONS
  • GLOBAL EXISTENCE
  • EXTERIOR DOMAIN
  • DIMENSIONS
  • GUIDES
  • BOUNDS

Cite this

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title = "Decay estimates of solutions to wave equations in conical sets",
abstract = "We consider the wave equation in an unbounded conical domain, with initial conditions and boundary conditions of Dirichlet or Neumann type. We give a uniform decay estimate of the solution in terms of weighted Sobolev norms of the initial data. The decay rate is the same as in the full space case.",
keywords = "decay estimates, fractional integrals, representation of solution, LINEAR EVOLUTION-EQUATIONS, SMALL AMPLITUDE SOLUTIONS, NONLINEAR HYPERBOLIC-EQUATIONS, KLEIN-GORDON EQUATIONS, GLOBAL EXISTENCE, EXTERIOR DOMAIN, DIMENSIONS, GUIDES, BOUNDS",
author = "Michael Dreher",
year = "2007",
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language = "English",
volume = "32",
pages = "477--501",
journal = "Communications in Partial Differential Equations",
issn = "0360-5302",
publisher = "Taylor & Francis",
number = "3",

}

Decay estimates of solutions to wave equations in conical sets. / Dreher, Michael.

In: Communications in Partial Differential Equations, Vol. 32, No. 3, 2007, p. 477-501.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Decay estimates of solutions to wave equations in conical sets

AU - Dreher, Michael

PY - 2007

Y1 - 2007

N2 - We consider the wave equation in an unbounded conical domain, with initial conditions and boundary conditions of Dirichlet or Neumann type. We give a uniform decay estimate of the solution in terms of weighted Sobolev norms of the initial data. The decay rate is the same as in the full space case.

AB - We consider the wave equation in an unbounded conical domain, with initial conditions and boundary conditions of Dirichlet or Neumann type. We give a uniform decay estimate of the solution in terms of weighted Sobolev norms of the initial data. The decay rate is the same as in the full space case.

KW - decay estimates

KW - fractional integrals

KW - representation of solution

KW - LINEAR EVOLUTION-EQUATIONS

KW - SMALL AMPLITUDE SOLUTIONS

KW - NONLINEAR HYPERBOLIC-EQUATIONS

KW - KLEIN-GORDON EQUATIONS

KW - GLOBAL EXISTENCE

KW - EXTERIOR DOMAIN

KW - DIMENSIONS

KW - GUIDES

KW - BOUNDS

U2 - 10.1080/03605300600718586

DO - 10.1080/03605300600718586

M3 - Article

VL - 32

SP - 477

EP - 501

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 3

ER -