Asymptotic properties of solutions to weakly dissipative wave equations below scaling

2004/06/25 by Jens Wirth, Wirth, Jens
Computer Science · Mathematics · #35B45 #35L15 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.math/0406515

openalex publication_date 2004/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to understand the influence of a dissipative term which is small in the sense that it is asymptotically below scaling on the asymptotic properties of solutions. A diagonalization procedure is applied in order to construct the main terms of the solution representation and this information is used to prove L^p--L^q decay estimates. Furthermore, the question of sharpness is considered and formulated in terms of a modified scattering theory.

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