Geodesic
About some classes of reverse tasks on determining the source function
Matematičeskie zametki SVFU, Tome 27 (2020) no. 1, pp. 21-40 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: second-order parabolic equation, inverse problem, initial-boundary value problem, well-posedness, unconditional solvability, uniqueness.
Mots-clés : existence 
@article{SVFU_2020_27_1_a1,
     author = {L. V. Neustroeva and S. G. Pyatkov},
     title = {About some classes of reverse tasks on determining the source function},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {21--40},
     year = {2020},
     volume = {27},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2020_27_1_a1/}
}
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L. V. Neustroeva; S. G. Pyatkov. About some classes of reverse tasks on determining the source function. Matematičeskie zametki SVFU, Tome 27 (2020) no. 1, pp. 21-40. http://geodesic.mathdoc.fr/item/SVFU_2020_27_1_a1/