Inverse problem of determining time-dependent leading coefficient in the time-fractional heat equation

2023/06/06 by Daurenbek Serikbaev, Michael Ruzhansky, Serikbaev, Daurenbek +3 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2306.03545

openalex publication_date 2023/06/06 · openalex created_date 2023/06/09 · openalex updated_date 2026/08/01

Abstract

In this paper, we investigate direct and inverse problems for the time-fractional heat equation with a time-dependent leading coefficient for positive operators. First, we consider the direct problem, and the unique existence of the generalized solution is established. We also deduce some regularity results. Here, our proofs are based on the eigenfunction expansion method. Second, we study the inverse problem of determining the leading coefficient, and the well-posedness of this inverse problem is proved.

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