### 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 language | English |
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Pages (from-to) | 393-402 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 112 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1991 |

Externally published | Yes |

### Keywords

- Decay estimate
- Wave equation

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Covachev, V., & Gueorguiev, V. S. (1991). Weighted decay estimate for the wave equation.

*Proceedings of the American Mathematical Society*,*112*(2), 393-402. https://doi.org/10.1090/S0002-9939-1991-1055769-7