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.
ASJC Scopus subject areas
- 数学 (全般)