An inequality regarding non-radiative linear waves via a geometric method

2022/01/07 by Liang Li, Li, Liang, Ruipeng Shen +3
Computer Science · Mathematics · #35L05 #44A12 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2201.02284

openalex publication_date 2022/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we consider the operator (T G) (x)= ∫_\mathbbS² G(x⋅ ω, ω) dω, x∈ ℝ³, G∈ L²(ℝ× \mathbbS²). This is the adjoint operator of the Radon transform. We manage to give an optimal L⁶ decay estimate of T G near the infinity by a geometric method, if the function G is compactly supported. As an application we give decay estimate of non-radiative solutions to the 3D linear wave equation in the exterior region \(x,t)∈ ℝ³ × ℝ: |x|>R+|t|\. This kind of decay estimate is useful in the channel of energy method for wave equations

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