Geodesic
An inverse problem for an equation of parabolic type
Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 595-600

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In this paper we consider an inverse problem for the differential equationu $$ t=u_{xx}+q(x, t)u; $$ the problem amounts to finding the coefficient $q(x,t)$ from the solution of a series of Cauchy problems for this equation, the solution being specified on some manifold. Our main result is a proof of a uniqueness theorem. 
@article{MZM_1976_19_4_a12,
     author = {V. G. Romanov},
     title = {An inverse problem for an equation of parabolic type},
     journal = {Matemati\v{c}eskie zametki},
     pages = {595--600},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a12/}
}
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V. G. Romanov. An inverse problem for an equation of parabolic type. Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 595-600. http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a12/