Geodesic
On determining the source function in heat and mass transfer problems under integral overdetermination conditions
Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 4, pp. 93-100

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We examine an inverse problem of determining the right-hand side (source function) in a parabolic equation from integral overdetermination data. By a solution to a parabolic equation we mean a weak solution, and the right-hand side in this equation can be a distribution of a certain class. Under some conditions on the data of the problem, we demonstrate that this inverse problem is well-posed and, in particular, stability estimates hold.
Keywords: inverse problem, second-order parabolic equation, boundary value problem, integral overdetermination condition, weak solution. 
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     author = {S. G. Pyatkov and M. V. Uvarova},
     title = {On determining the source function in heat and mass transfer problems under integral overdetermination conditions},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {93--100},
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     year = {2016},
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     url = {http://geodesic.mathdoc.fr/item/SJIM_2016_19_4_a9/}
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S. G. Pyatkov; M. V. Uvarova. On determining the source function in heat and mass transfer problems under integral overdetermination conditions. Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 4, pp. 93-100. http://geodesic.mathdoc.fr/item/SJIM_2016_19_4_a9/