Large Time Behavior for the Classical Wave Equation With Different Regular Data and Its Applications
Abstract
In this article, we mainly consider large time behavior for the classical free wave equation u t t − Δ u = 0 in R n . We derive some large time optimal estimates for the quantity of solution ‖ u ( t , ⋅ ) ‖ L 2 with initial data belonging to L 2 or with additional weighted L 1 integrabilities. Particularly, some thresholds are discovered for the (local or global in time) stabilization of this quantity. We also apply these results to the wave equation with scale-invariant terms, the undamped σ -evolution equation, the critical Moore–Gibson–Thompson equation, and the linearized compressible Euler system.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Publication details
- Journal / source
- Asymptotic Analysis
- Publisher
- SAGE Publications
- Volume
- 150
- Issue
- 4
- Pages
- 1638-1659
- Publication date
- 16 April 2026
- Language
- EN