Geodesic
On the inverse problem of determining the lowest coefficient depending on the space variable in a parabolic equation with weak degeneracy
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 1, Tome 206 (2022), pp. 68-81

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In this paper, we prove existence and uniqueness theorems for solutions of the inverse problem of determining the $x$-dependent absorption coefficient in a degenerate parabolic equation. As an additional condition, the integral observation condition is specified. Also, we give examples of inverse problems satisfying the conditions of the theorems proved in the paper.
Keywords: inverse problem, integral observation, degenerate parabolic equation. 
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     author = {V. L. Kamynin},
     title = {On the inverse problem of determining the lowest coefficient depending on the space variable in a parabolic equation with weak degeneracy},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {68--81},
     publisher = {mathdoc},
     volume = {206},
     year = {2022},
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V. L. Kamynin. On the inverse problem of determining the lowest coefficient depending on the space variable in a parabolic equation with weak degeneracy. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 1, Tome 206 (2022), pp. 68-81. http://geodesic.mathdoc.fr/item/INTO_2022_206_a6/