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

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