Geodesic
Controllability and exact controllability in a problem of heat transfer with convection and time distributed functional
Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 32 (2019) no. 32, pp. 57-71

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We consider a temperature control problem based on the heat equation with a convective term and a quadratic quality functional. We examine the structure of the set of attainable functions and establish controllability of the problem on various sets of admissible controls. 
@article{TSP_2019_32_32_a2,
     author = {I. V. Astashova and A. V. Filinovskiy},
     title = {Controllability and exact controllability in a problem of heat transfer with convection and time distributed functional},
     journal = {Trudy Seminara im. I.G. Petrovskogo},
     pages = {57--71},
     publisher = {mathdoc},
     volume = {32},
     number = {32},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a2/}
}
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I. V. Astashova; A. V. Filinovskiy. Controllability and exact controllability in a problem of heat transfer with convection and time distributed functional. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 32 (2019) no. 32, pp. 57-71. http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a2/