Controllability of parabolic equations
Sbornik. Mathematics, Tome 186 (1995) no. 6, pp. 879-900 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper studies two problems of exact controllability of semilinear parabolic equations. In the first, the control is on the right-hand side of the parabolic equation and distributed over an arbitrary subdomain $\omega$ of the domain $\Omega$. In the second, the control is contained in the boundary conditions and distributed over a subdomain $\Gamma_0$ of the boundary $\partial\Omega$. If the original data satisfy certain conditions, then both problems are solvable.
@article{SM_1995_186_6_a5,
     author = {Yu. S. \`Emanuilov},
     title = {Controllability of parabolic equations},
     journal = {Sbornik. Mathematics},
     pages = {879--900},
     year = {1995},
     volume = {186},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_6_a5/}
}
TY  - JOUR
AU  - Yu. S. Èmanuilov
TI  - Controllability of parabolic equations
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 879
EP  - 900
VL  - 186
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/SM_1995_186_6_a5/
LA  - en
ID  - SM_1995_186_6_a5
ER  - 
%0 Journal Article
%A Yu. S. Èmanuilov
%T Controllability of parabolic equations
%J Sbornik. Mathematics
%D 1995
%P 879-900
%V 186
%N 6
%U http://geodesic.mathdoc.fr/item/SM_1995_186_6_a5/
%G en
%F SM_1995_186_6_a5
Yu. S. Èmanuilov. Controllability of parabolic equations. Sbornik. Mathematics, Tome 186 (1995) no. 6, pp. 879-900. http://geodesic.mathdoc.fr/item/SM_1995_186_6_a5/

[1] Russell D. L., “Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions”, SIAM Review, 20:4 (1978), 639–739 | DOI | MR | Zbl

[2] Russell D. L., “A unified boundary controllability theory”, Studies in Applied Math., 52:3 (1973), 189–211 | MR | Zbl

[3] Fattorini H. O., “Boundary control of temperature distributions in a parallelepiped”, SIAM J. Control, 13:1 (1975), 1–13 | DOI | MR | Zbl

[4] Fabre C., Puel J.-P., Zuazua E., “Controllabilite approchee de l'equation de la chaleur semilineaire”, C. R. Acad. Sci. Paris, 315:1 (1992), 807–812 | MR | Zbl

[5] Landis E. M., “O povedenii resheniya parabolicheskogo uravneniya na kharakteristike”, Matem. zametki, 12:3 (1972), 257–262 | MR | Zbl

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

[7] Emanuilov O. Yu., “Granichnaya upravlyaemost parabolicheskimi uravneniyami”, UMN, 48:3 (1993), 211–212 | MR

[8] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, T. 3, Mir, M., 1987 | MR

[9] Emanuilov O. Yu., “Tochnaya upravlyaemost polulineinymi parabolicheskimi uravneniyami”, Vestnik RUDN. Ser. matematika, 1994, no. 1, 109–116 | MR | Zbl

[10] Fursikov A. V., Imanuilov O. Yu., “On exact boundary zero-controllability of two-dimensional Navier–Stokes equation”, Acta Applicande Mathematicae, 37 (1994), 67–76 | DOI | MR | Zbl

[11] Fursikov A. V., Imanuilov O. Yu., “On controllability of certain systems simulating a fluid flow”, IMA Volumes in Mathematics and its Applications, 68, 149–184 | MR | Zbl

[12] Fursikov A. V., “Svoistva reshenii nekotorykh ekstremalnykh zadach, svyazannykh s sistemoi Nave–Stoksa”, Matem. sb., 118 (160):3 (1982), 323–349 | MR | Zbl

[13] Fursikov A. V., “O nekotorykh zadachakh upravleniya i o rezultatakh, kasayuschikhsya odnoznachnoi razreshimosti smeshannoi kraevoi zadachi dlya trekhmernykh sistem Nave–Stoksa i Eilera”, DAN SSSR, 252:5 (1980), 1066–1070 | MR | Zbl

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

[15] Oben Zh.-P., Ekland I., Prikladnoi nelineinyi analiz, Mir, M., 1988 | MR