About some classes of reverse tasks on determining the source function

  • Neustroeva Lyubov V., starkovaLV@mail.ru Yugra State University, 16 Chekhov Street, Khanty-Mansiisk, Russia 628012
  • Pyatkov Sergey G., s_pyatkov@ugrasu.ru Yugra State University, 16 Chekhov Street, Khanty-Mansiisk, Russia 628012; Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, Novosibirsk 630090, Russia
Keywords: second-order parabolic equation, inverse problem, initial-boundary value problem, well-posedness, unconditional solvability, existence, uniqueness

Abstract

We examine the questions of solvability, uniqueness, and some qualitative properties of solutions of inverse problems of determining point sources (the right-hand side of a special form) in a one-dimensional parabolic equation. The values of the solution at a collection of points are taken as the overdetermination data. Examples are displayed showing that the uniqueness fails without additional conditions on the mutual location of sources and measurement points. An asymptotic formula for determining the coordinates of one source from two measurements is obtained.

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How to Cite
Neustroeva, L. and Pyatkov, S. (2020) “About some classes of reverse tasks on determining the source function”, Mathematical notes of NEFU, 27(1), pp. 21-40. doi: https://doi.org/10.25587/SVFU.2020.77.95.002.
Section
Mathematics