An inverse problem for the heat equation

2001/02/22 by A. G. Ramm, А. Г. Рамм, Ramm, A. G. · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #35R30 #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:35R30

paper · pdf · doi:10.48550/arxiv.math-ph/0102029

arxiv created 2001/02/22 · openalex publication_date 2001/02/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let u_t = u_xx - q(x) u, 0 ≤ x ≤ 1, t>0, u(0, t) = 0, u(1, t) = a(t), u(x,0) = 0, where a(t) is a given function vanishing for t>T, a(t) \not≡ 0, ∫^T₀ a(t) dt < ∞. Suppose one measures the flux u_x (0,t) := b₀ (t) for all t>0. Does this information determine q(x) uniquely? Do the measurements of the flux u_x (1,t) := b(t) give more information about q(x) than b₀ (t) does? The above questions are answered in this paper.

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