Modified scattering for a wave equation with weak dissipation

2005/09/10 by Jens Wirth, Wirth, Jens
Computer Science · Mathematics · #35B45 #35L15 #35L50 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical methods in inverse problems #math.AP #math.CA #msc:35B45 #msc:35L15 #msc:35L50

paper · pdf · doi:10.48550/arxiv.math/0509229

7 pages

arxiv created 2005/09/10 · openalex publication_date 2005/09/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem for the weakly dissipative wave equation \square u+\fracμ1+t u_t=0 with parameter μ≥2. Based on the explicit representations of solutions provided in [Math. Meth. Appl. Sci. 2004; \bf 27:101-124] sharp decay estimates for data from a dense subspace of the energy space are derived. Furthermore, sharpness is discussed in terms of a modified scattering theory.

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