Geodesic
Parabolic equations with an unknown time-dependent coefficient
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 12, pp. 2168-2184 Cet article a éte moissonné depuis la source Math-Net.Ru

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The solvability of nonlinear inverse problems of determining the solution $u(x,t)$ and the coefficients $p(t)$ and $q(t)$ in parabolic equations subject to the boundary conditions of the first or second initial-boundary value problems and an integral overdetermination condition is investigated. Existence theorems for the regular solution are proved. 
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A. I. Kozhanov. Parabolic equations with an unknown time-dependent coefficient. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 12, pp. 2168-2184. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a6/

[1] Prilepko A. I., Orlovskii D. G., “Obratnye zadachi dlya evolyutsionnykh polulineinykh uravnenii”, Dokl. AN SSSR, 277:4 (1984), 799–803 | MR | Zbl

[2] Prilepko A. I., Orlovskii D. G., “Ob opredelenii parametra evolyutsionnogo uravneniya i obratnykh zadachakh matematicheskoi fiziki”, Differents. ur-niya, 21:4 (1985), 694–700 | MR

[3] Cannon I. R., Lin Y., “Determination of a parameter $p(t)$ in some qiuasi-linear parabolic differential equations”, Inverse Problems, 4 (1988), 35–45 | DOI | MR | Zbl

[4] Kamynin V. L., Saroldi M., “Nelineinaya obratnaya zadacha dlya parabolicheskogo uravneniya vysokogo poryadka”, Zh. vychisl. matem. i matem. fiz., 38:10 (1998), 1683–1691 | MR | Zbl

[5] Ivanchov N. I., “Nekotorye obratnye zadachi dlya uravneniya teploprovodnosti s nelokalnymi kraevymi usloviyami”, Ukrainskii matem. zhurn., 45:8 (1993), 1066–1071 | MR | Zbl

[6] Ivanchov N. I., “Ob opredelenii zavisyaschego ot vremeni starshego koeffitsienta v parabolicheskom uravnenii”, Sibirskii matem. zhurnal, 39:3 (1998), 539–550 | MR | Zbl

[7] Ivanchov M. I., Pobirivska N. V., “Odnochasne viznachennya dvokh koeffitsientiv u parabolichnomu rivnyanni u vipadku nelokalnykh ta integralnikh umov”, Ukrainskii matem. zhurnal, 53:5 (2001), 589–596 | MR | Zbl

[8] Ivanchov M. I., “Reduktsiya zadachi z vilnoyu mezheyu dlya papabolichnogo rivnyannya do obernenoi zadachi”, Nelineinye granichnye zadachi, 12, In-t prikl. matem. i mekhan., Donetsk, 2002, 73–83

[9] Ivanchov M. I., “Obernena zadacha z vilnoyu mezheyu dlya rivnyannya teploprovodnosti”, Ukrainskii matem. zhurnal, 55:7 (2003), 901–910 | MR | Zbl

[10] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR

[11] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vyssh. shk., M., 1995 | Zbl

[12] Dzhenaliev M. T., K teorii lineinykh kraevykh zadach dlya nagruzhennykh differentsialnykh uravnenii, In-t teor. i prikl. matem., Almaty, 1995

[13] Yakubov S. Ya., Lineinye differentsialno-operatornye uravneniya i ikh prilozheniya, Elm, Baku, 1985

[14] Kozhanov A. I., Composite type equations and inverse problems, VSP, Utrecht, 1999 | MR | Zbl

[15] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Nauka, M., 1988 | MR

[16] Krein S. G. (red.), Funktsionalnyi analiz, Nauka, M., 1964