Weighted decay estimate for the wave equation

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1 Citation (Scopus)

Abstract

The work is devoted to the proof of a new L∞-L weighted estimate for the solution to the nonhomogeneous wave equation in (3 + l)-dimensional space-time. The weighted Sobolev spaces are associated with the generators of the Poincarégroup. The estimate obtained is applied to prove the global existence of a solution to a nonlinear system of wave and Klein-Gordon equations with small initial data.

Original languageEnglish
Pages (from-to)393-402
Number of pages10
JournalProceedings of the American Mathematical Society
Volume112
Issue number2
DOIs
Publication statusPublished - 1991
Externally publishedYes

Keywords

  • Decay estimate
  • Wave equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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