Morawetz type estimate for damped wave equation in ℝⁿ (n≥ 4) and its application

2025/05/08 by Daoyin He, He, Daoyin, N. Lai +1
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2505.05268

Abstract

In this paper we establish a Morawetz type etimate for the linear inhomogeneous wave equation with time-dependent scale invariant damping in ℝⁿ (n≥ 4). The novelty is that we view the differential operator \Box+\fracμt∂_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 ∂_t²u-Δu+(∂_tu)/(t)=|u|^p,~~~tgt;t₀≥ 0 is obtained in ℝⁿ (n≥ 4).

Citations

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• Global existence for small amplitude semilinear wave equations with time-dependent scale-invariant damping