2014/12/26 by Sergey Leble, Leble, Sergey, И. С. Верещагина +2 · 1 citation
Computer Science · Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #34A55 #Applied mathematics #Cauchy problem #Computer science #Conservation law #Dissipation #Entropy (arrow of time) #FOS: Physical sciences #Image and Signal Denoising Methods #Initial value problem #Inverse problem #Law #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Norm (philosophy) #Numerical methods in inverse problems #Operator (biology) #Physics #Regularization (linguistics) #Ultrasonics and Acoustic Wave Propagation #Underwater Acoustics Research #Wave equation #math-ph #math.MP #msc:34A55
paper · pdf · doi:10.48550/arxiv.1412.7926
published in arXiv (Cornell University) (Cornell University) · 11 pages, Kaliningrad, "Inverse Problem and Integral Geometry" conference 2014, oktober
arxiv created 2014/12/26 · openalex publication_date 2014/12/26 · arxiv updated 2014/12/30 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28
A problem of a wave identification is formulated. An example is considered in\nconditions of one-dimensional Cauchy problem for conventional string equation\nin matrix form and its inhomogeneous two-component version. The acoustic and\nelectromagnetic problems are discussed within the restrictions outlined. The\nprojecting operator technique is used to split the solution space and analyze\ninput of a wave monitoring in vicinity of an observation point. The solution\nspace is supplied by L2 norm via the problem conservation law; its\nfinite-dimensional analog is used as a measure of a given mode presence and\ninformation about form. The algorithm of the problem solution is presented in\nterms of appropriate regularization to reconstruct an incoming pulses origin.\nThe dissipation and entropy mode account in the problem of acoustic waves\nextraction is also discussed in terms of correspondent projecting technique.\n