### 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 |
---|---|

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 |

### Fingerprint

### Keywords

- Decay estimate
- Wave equation

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*112*(2), 393-402. https://doi.org/10.1090/S0002-9939-1991-1055769-7

**Weighted decay estimate for the wave equation.** / Covachev, Valery; Gueorguiev, Vladimir Simeonov.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 112, no. 2, pp. 393-402. https://doi.org/10.1090/S0002-9939-1991-1055769-7

}

TY - JOUR

T1 - Weighted decay estimate for the wave equation

AU - Covachev, Valery

AU - Gueorguiev, Vladimir Simeonov

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

KW - Decay estimate

KW - Wave equation

UR - http://www.scopus.com/inward/record.url?scp=84968503798&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968503798&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1991-1055769-7

DO - 10.1090/S0002-9939-1991-1055769-7

M3 - Article

VL - 112

SP - 393

EP - 402

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -