2015/01/30 by Martin Lazar, Lazar, Martin
Computer Science · Engineering · Mathematics · #93B05 #93B07 #93C20 #93D09 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #math.AP #msc:93B05 #msc:93B07 #msc:93C20 #msc:93D09
paper · pdf · doi:10.48550/arxiv.1502.00663
arxiv created 2015/01/30 · openalex publication_date 2015/01/30 · arxiv updated 2015/02/04 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We analyse stability of observability estimates for solutions to wave and Scr" odinger equations subjected to additive perturbations. The paper generalises the recent averaged observability/control result by allowing for systems consisting of operators of different types. The method also applies to the simultaneous observability problem by which one tries to estimate the energy of each component of a system under consideration. The analysis relies on microlocal defect tools; in particular on standard H-measures, when the main dynamic of the system is governed by the wave operator, while parabolic H-measures are explored in the case of the Schr" odinger operator.