Inverse problems for parabolic equations 2

2005/10/04 by A. G. Ramm, А. Г. Рамм, Ramm, A. G.
Computer Science · Mathematics · #35K20 #35R30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #math.AP #msc:35K20 #msc:35R30

paper · pdf · doi:10.48550/arxiv.math/0510076

arxiv created 2005/10/04 · openalex publication_date 2005/10/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let u_t-u_xx=h(t) in 0≤ x ≤ π, t≥ 0. Assume that u(0,t)=v(t), u(π,t)=0, and u(x,0)=g(t). The problem is: \it what extra data determine the three unknown functions \h, v, g\ uniquely?. This question is answered and an analytical method for recovery of the above three functions is proposed.

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