Geodesic
Recovering a source function in a one-dimensional parabolic equation with dead zones taking into account
Matematičeskie zametki SVFU, Tome 23 (2016), pp. 46-57

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We examine the question of well-posedness in the Sobolev spaces of an inverse problem of determining a source function in a system comprising a parabolic equation and an ordinary differential equation. The overdetermination conditions are the values of concentration of an admixture at separate points. We prove existence and uniqueness of solutions to the problem.
Mots-clés : parabolic equation
Keywords: inverse problem, heat-and-mass transfer, boundary value problem, source function. 
@article{SVFU_2016_23_a3,
     author = {S. G. Pyatkov and V. V. Rotko},
     title = {Recovering a source function in a one-dimensional parabolic equation with dead zones taking into account},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {46--57},
     publisher = {mathdoc},
     volume = {23},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2016_23_a3/}
}
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S. G. Pyatkov; V. V. Rotko. Recovering a source function in a one-dimensional parabolic equation with dead zones taking into account. Matematičeskie zametki SVFU, Tome 23 (2016), pp. 46-57. http://geodesic.mathdoc.fr/item/SVFU_2016_23_a3/