Geodesic
On solvability of the inverse problem for the one-dimensional parabolic equation with unknown time-dependent coefficient under integral observation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 28 (2022) no. 3-4, pp. 7-17

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In this article, we study the inverse problem of determination of time-dependent coefficient in the parabolic equation. We prove existence and uniqueness theorem for the solution of the inverse problem with nonlocal boundary conditions and integral observation. The proof is based on a priori estimates obtained in this article and the results on solvability of corresponding direct problem for the equarion under consideration.
Keywords: inverse problem, time-dependent unknown coefficient, integral observation, nonlocal boundary conditions. 
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     author = {A. V. Bogatov and L. S. Pulkina},
     title = {On solvability of the inverse problem for the one-dimensional parabolic equation with unknown time-dependent coefficient under integral observation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
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     publisher = {mathdoc},
     volume = {28},
     number = {3-4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2022_28_3-4_a0/}
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A. V. Bogatov; L. S. Pulkina. On solvability of the inverse problem for the one-dimensional parabolic equation with unknown time-dependent coefficient under integral observation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 28 (2022) no. 3-4, pp. 7-17. http://geodesic.mathdoc.fr/item/VSGU_2022_28_3-4_a0/