Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SEMR_2014_11_a64, author = {S. G. Pyatkov and E. I. Safonov}, title = {On some classes of linear inverse problems for parabolic systems of equations}, journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a}, pages = {777--799}, publisher = {mathdoc}, volume = {11}, year = {2014}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a64/} }
TY - JOUR AU - S. G. Pyatkov AU - E. I. Safonov TI - On some classes of linear inverse problems for parabolic systems of equations JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2014 SP - 777 EP - 799 VL - 11 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SEMR_2014_11_a64/ LA - ru ID - SEMR_2014_11_a64 ER -
S. G. Pyatkov; E. I. Safonov. On some classes of linear inverse problems for parabolic systems of equations. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 777-799. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a64/
[1] G. V. Alekseev, Optimizatsiya v statsionarnykh zadachakh teplomassoperenosa i magnitnoi gidrodinamiki, Nauchnyi mir, M., 2010
[2] Yu. Ya. Belov, Inverse problems for parabolic equations, VSP, Utrecht, 2002 | MR | Zbl
[3] M. Levandowsky, W. S. Childress, S. H. Hunter, E. A. Spiegel, “A mathematical model of pattern formation by swimming microorganisms”, J. Protozoology, 22 (1975), 296–309 | DOI
[4] A. Capatina, R. Stavre, “A control problem in biconvective flow”, J. Math. Kyoto Univ., 37:4 (1997), 585–595 | MR | Zbl
[5] G. V. Alekseev, E. A. Kalinina, “Identifikatsiya mladshego koeffitsienta dlya statsionarnogo uravneniya konvektsii-diffuzii-reaktsii”, Sib. zhur. industrialnoi matematiki, 10 (2007), 3–16 | MR | Zbl
[6] G. V. Alekseev, “Coefficient Inverse Extremum Problems for Stationary Heat and Mass Transfer Equations”, Comp. Math. and Math. Phys., 47:6 (2007), 1007–1028 | DOI | MR | Zbl
[7] O. M. Babeshko, O. V. Evdokimova, S. M. Evdokimov, “On taking into account the types of sources and settling zones of pollutants”, Dokl. Math., 61:2 (2000), 283–285 | MR | Zbl
[8] E. A. Kalinina, “Chislennoe issledovanie obratnoi zadachi vosstanovleniya plotnosti istochnika dvumernogo nestatsionarnogo uravneniya konvektsii-diffuzii”, Dalnevostochnyi matem. zhur., 5:1 (2004), 89–99
[9] Yu. A. Kriksin, S. N. Plyuschev, E. A. Samarskaya, V. F. Tishkin, “Obratnaya zadacha vosstanovleniya plotnosti istochnika dlya uravneniya konvektsii-diffuzii”, Matem. modelirovanie, 7:11 (1995), 95–108 | MR | Zbl
[10] A. D. Iskenderov, A. Ya. Akhundov, “Inverse problem for a linear system of parabolic equations”, Doklady Mathematics, 79:1 (2009), 73–75 | DOI | MR | Zbl
[11] M. I. Ismailov, F. Kanca, “Inverse problem of finding the time-dependent coefficient of heat equation from integral overdetermination condition data”, Inverse Problems In Science and Engineering, 20:4 (2012), 463–476 | DOI | MR | Zbl
[12] M. I. Ivanchov, “Inverse problem of simulataneous determination of two coefficients in a parabolic equation”, Ukrainian Math. J., 52:3 (2000), 379–387 | DOI | MR | Zbl
[13] Li Jing, Xu Youjun, “An inverse coefficient problem with nonlinear parabolic equation”, J. Appl. Math. Comput., 34:1–2 (2010), 195–206 | DOI | MR | Zbl
[14] V. L. Kamynin, E. Franchini, “An inverse problem for a higher-order parabolic equation”, Mathematical Notes, 64:5–6 (1998), 590–599 | DOI | MR | Zbl
[15] N. B. Kerimov, M. I. Ismailov, “An inverse coefficient problem for the heat equation in the case of nonlocal boundary conditions”, Journal of Mathematical Analysis and Applications, 396:2 (2012), 546–554 | DOI | MR | Zbl
[16] A. I. Kozhanov, “Parabolicheskie uravneniya s neizvestnym koeffitsientom, zavisyaschim ot vremeni”, Zh. Vychisl. Matem. i matem. fiz., 45:12 (2005), 2168–2184 | MR | Zbl
[17] I. A. Vasin, V. L. Kamynin, “On the asymptotic behavior of solutions to inverse problems for parabolic equations”, Siberian Mathematical Journal, 38:4 (1997), 647–662 | DOI | MR | Zbl
[18] A. I. Prilepko, D. G. Orlovsky, I. A. Vasin, Methods for solving inverse problems in Mathematical Physics, Marcel Dekker, Inc., New-York, 1999 | MR
[19] A. P. Tryanin, “Determination of heat-transfer coefficients at the inlet into a porous body and inside it by solving the inverse problem”, Inzhenerno-Fizicheskii Zhurnal, 52:3 (1987), 469–475
[20] M. Dehghan, F. Shakeri, “Method of lines solutions of the parabolic inverse problem with an overspecification at a points”, Numer Algor., 50:4 (2009), 417–437 | DOI | MR | Zbl
[21] M. Dehghan, “Numerical computation of a control function in a partial differential equation”, Applied mathematics and computation, 147:2 (2004), 397–408 | DOI | MR | Zbl
[22] O. M. Alifanov, E. A. Artyukhov, A. V. Nenarokom, Obratnye zadachi slozhnogo teploobmena, Yanus-K, M., 2009
[23] O. M. Alifanov, Inverse Heat Transfer Problems, Springer-Verlag, Berlin–Heidelberg, 1994 | Zbl
[24] M. N. Ozisik, H. A. B. Orlando, Inverse heat transfer, Taylor Francis, New-York, 2000
[25] S. G. Pyatkov, M. L. Samkov, “On some classes of coefficient inverse problems for parabolic systems of equations”, Sib. Adv. in Math., 22:4 (2012), 287–302 | DOI | MR | Zbl
[26] S. G. Pyatkov, “On some classes of inverse problems for parabolic equations”, J. Inv. Ill-Posed problems, 18:8 (2011), 917–934 | DOI | MR
[27] M. Ivanchov, Inverse problems for equations of parabolic type, Math. Studies. Monograph Series, 10, 2003 | MR | Zbl
[28] S. I. Kabanikhin, Obratnye i nekorektnye zadachi, Sibirskoe nauchnoe izdatelstvo, Novosibirsk, 2009
[29] Kh. Tribel, Teoriya interpolyatsii. Funktsionalnye prostranstva. Differentsialnye operatory, Mir, M., 1980 | MR
[30] H. Amann, “Compact embeddings of vector-valued Sobolev and Besov spaces”, Glasnik matematicki, 35(55):1 (2000), 161–177 | MR | Zbl
[31] H. Amann, “Operator-valued Foutier multipliers, vector-valued Besov spaces and applications”, Mathem. Nachr., 186:1 (1997), 5–56 | DOI | MR | Zbl
[32] H. Amann, Linear and Quasilinear Parabolic Problems, v. I, Birkhauser Verlag, Basel–Boston–Berlin, 1995 | MR | Zbl
[33] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967 | MR | Zbl
[34] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR
[35] S. G. Pyatkov, B. N. Tsybikov, “On some classes of inverse problems for parabolic and elliptic equations”, J. Evol. Equat., 11:1 (2011), 155–186 | DOI | MR | Zbl