Scattering problems for symmetric systems with dissipative boundary conditions

2012/06/14 by Vesselin Petkov, Petkov, Vesselin
Mathematics · Physics and Astronomy · #35L50 #35P25 #47A40 #81U40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.FA #math.MP #msc:35L50 #msc:35P25 #msc:47A40 #msc:81U40

paper · pdf · doi:10.48550/arxiv.1206.3017

openalex publication_date 2012/06/14 · arxiv created 2013/02/07 · arxiv updated 2013/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study symmetric systems with dissipative boundary conditions. The solutions of the mixed problems for such systems are given by a contraction semigroup V(t)f = e^tG_bf, t ≥ 0. The solutions u(t, x) = V(t)f, where f is an eigenfunction of the generator G_b with eigenvalue λ,\Re λ< 0, are called asymptotically disappearing (ADS). We prove that the wave operators are not complete if there exist (ADS). This is the case for Maxwell system with special boundary conditions in the exterior of the sphere. We obtain a representation of the scattering kernel and we examine the inverse back-scattering problem related to the leading term of the scattering kernel.

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