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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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},
     year = {2019},
     volume = {32},
     number = {32},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a2/}
}
TY  - JOUR
AU  - I. V. Astashova
AU  - A. V. Filinovskiy
TI  - Controllability and exact controllability in a problem of heat transfer with convection and time distributed functional
JO  - Trudy Seminara im. I.G. Petrovskogo
PY  - 2019
SP  - 57
EP  - 71
VL  - 32
IS  - 32
UR  - http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a2/
LA  - ru
ID  - TSP_2019_32_32_a2
ER  - 
%0 Journal Article
%A I. V. Astashova
%A A. V. Filinovskiy
%T Controllability and exact controllability in a problem of heat transfer with convection and time distributed functional
%J Trudy Seminara im. I.G. Petrovskogo
%D 2019
%P 57-71
%V 32
%N 32
%U http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a2/
%G ru
%F TSP_2019_32_32_a2
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/

[1] Egorov Yu.V., “Nekotorye zadachi teorii optimalnogo upravleniya”, Zh. vychisl. matem. i matem. fiz., 3:5 (1963), 887–904

[2] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972

[3] Butkovskii A. G., Teoriya optimalnogo upravleniya sistemami s raspredelennymi parametrami, Nauka, M., 1965

[4] Friedman A., “Optimal control for parabolic equations”, J. Math. Anal. Appl., 18:3 (1967), 479–491 | DOI | Zbl

[5] Lions Zh.-L., Upravlenie singulyarnymi raspredelennymi sistemami, Fizmatlit, M., 1987

[6] Butkovsky A. G., Egorov A. I., Lurie K. A., “Optimal control of distributed systems (a survey of soviet publications)”, SIAM J. Control., 6:3 (1968), 437–476 | DOI | MR | Zbl

[7] Butkovskii A. G., “Optimalnye protsessy v sistemakh s raspredelennymi parametrami”, Avtom. i telemekh., 22:1 (1961), 17–26

[8] Egorov A. I., Optimalnoe upravlenie teplovymi i diffuzionnymi protsessami, Nauka, M., 1978

[9] Troltzsch F., Optimal Control of Partial Differential Equations. Theory, Methods and Applications, Grad. Stud. Math., 112, AMS, Providence, 2010 | DOI | MR | Zbl

[10] Farag M. H., Talaat T. A., Kamal E. M., “Existence and uniqueness solution of a class of quasilinear parabolic boundary control problems”, Cubo, 15:2 (2013), 111–119 | DOI | MR | Zbl

[11] Astashova I. V., Filinovskiy A. V., Lashin D. A., “On maintaining optimal temperatures in greenhouses”, WSEAS Trans. Circuits Systems, 15:23 (2016), 198–204

[12] Astashova I. V., Filinovskiy A. V., Lashin D. A., “On optimal temperature control in hothouses”, Proc. Int. Conf. on Numerical Analysis and Applied Mathematics (2016), AIP Conf. Proc., 2017, 4–8

[13] Astashova I. V., Filinovskii A. V., “Ob upravlyaemosti v parabolicheskoi zadache s raspredelennym po vremeni funktsionalom”, Differents. uravn., 53 No6 (2018), 851–853

[14] Astashova I. V., Filinovskiy A. V., Kondratiev V. A., Muravei L. A., “Some problems in the qualitative theory of differential equations”, J. Nat. Geom., 23:1–2 (2003), 1–126 | MR | Zbl

[15] Astashova I. V., Kachestvennye svoistva reshenii differentsialnykh uravnenii i smezhnye voprosy spektralnogo analiza, ed. I. V. Astashova, YuNITI-DANA, M., 2012

[16] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Fizmatlit, M., 1973

[17] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967 | MR

[18] Ilin A. M., Kalashnikov A. S., Oleinik O. A., “Lineinye uravneniya vtorogo poryadka parabolicheskogo tipa”, UMN, 17:3 (1962), 3–146 | MR | Zbl

[19] Landis E. M., Oleinik O. A., “Obobschennaya analitichnost i svyazannye s nei svoistva reshenii ellipticheskikh i parabolicheskikh uravnenii”, UMN, 29:2 (1974), 190–206 | MR | Zbl

[20] Lyusternik L. A., Sobolev V. I., Elementy funktsionalnogo analiza, Fizmatlit, M., 1965, 519 pp. | MR

[21] Titchmarsh E. C., “The zeros of certain integral functions”, Proc. Lond. Math. Soc., s2–25:1 (1926), 283–302 | DOI | MR | Zbl

[22] Evans L. K., Uravneniya s chastnymi proizvodnymi, Universitet. ser., 7, Tamara Rozhkovskaya, Novosibirsk, 1998