Geodesic
Optimal Recovery of Pipe Temperature from Inaccurate Measurements
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 216-223

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The problem of optimal recovery of the solution of the heat equation on a manifold at a given instant of time from inaccurate measurements of this solution at other instants of time is considered, the manifold being the product of the real line and a circle. A family of optimal recovery methods is constructed. 
@article{TM_2021_312_a11,
     author = {G. G. Magaril-Il'yaev and K. Yu. Osipenko and E. O. Sivkova},
     title = {Optimal {Recovery} of {Pipe} {Temperature} from {Inaccurate} {Measurements}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {216--223},
     publisher = {mathdoc},
     volume = {312},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_312_a11/}
}
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G. G. Magaril-Il'yaev; K. Yu. Osipenko; E. O. Sivkova. Optimal Recovery of Pipe Temperature from Inaccurate Measurements. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 216-223. http://geodesic.mathdoc.fr/item/TM_2021_312_a11/