Morawetz type estimate for damped wave equation in high dimension and its application
Abstract
Abstract In this paper we establish a Morawetz type estimate for the linear inhomogeneous wave equation with time-dependent scale invariant damping in R n ( n ⩾ 4 ) . The novelty is that we view the differential operator ◻ + μ t ∂ t as n + 1 + μ dimensional operator, then a well-matched multiplier is introduced. As an application, a sharp global existence result for the small data Cauchy problem of the semilinear wave equation ∂ t 2 u − Δ u + ∂ t u t = | u | p , t > t 0 ⩾ 0 with µ = 1 is obtained in R n ( n ⩾ 4 ) .
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Advanced Mathematical Physics Problems
Numerical methods in inverse problems
Publication details
- Journal / source
- Nonlinearity
- Publisher
- IOP Publishing
- Volume
- 39
- Issue
- 8
- Pages
- 085020–085020
- Publication date
- 12 August 2026