2020/10/27 by M. N. Demchenko, Demchenko, M. N.
Computer Science · Engineering · Mathematics · #35R25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #math.AP #msc:35R25
paper · pdf · doi:10.48550/arxiv.2010.14354
arxiv created 2020/10/27 · openalex publication_date 2020/10/27 · arxiv updated 2020/10/28 · openalex created_date 2020/11/09 · openalex updated_date 2026/07/28
The subject of the paper is the Cauchy problem for the wave equation in a space-time cylinder Ω×\mathbb R, Ω⊂\mathbb R2, with the data on the surface ∂Ω× I, where I is a finite time interval. The algorithm for solving the Cauchy problem with the data on S× I, S⊂∂Ω, was obtained previously. Here we adapt this algorithm to the special case S=∂Ω and show that in this situation, the solution is determined with higher stability in comparison with the case S\subsetneqq∂Ω.