Geodesic
On the Unique Solvability of an Inverse Problem for Parabolic Equations under a Final Overdetermination Condition
Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 217-227 
V. L. Kamynin. On the Unique Solvability of an Inverse Problem for Parabolic Equations under a Final Overdetermination Condition. Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 217-227. http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a5/
@article{MZM_2003_73_2_a5,
     author = {V. L. Kamynin},
     title = {On the {Unique} {Solvability} of an {Inverse} {Problem} for {Parabolic} {Equations} under a {Final} {Overdetermination} {Condition}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {217--227},
     year = {2003},
     volume = {73},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a5/}
}
TY  - JOUR
AU  - V. L. Kamynin
TI  - On the Unique Solvability of an Inverse Problem for Parabolic Equations under a Final Overdetermination Condition
JO  - Matematičeskie zametki
PY  - 2003
SP  - 217
EP  - 227
VL  - 73
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a5/
LA  - ru
ID  - MZM_2003_73_2_a5
ER  - 
%0 Journal Article
%A V. L. Kamynin
%T On the Unique Solvability of an Inverse Problem for Parabolic Equations under a Final Overdetermination Condition
%J Matematičeskie zametki
%D 2003
%P 217-227
%V 73
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a5/
%G ru
%F MZM_2003_73_2_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the unique solvability of the inverse problem of determining the right-hand side of a parabolic equation with the leading coefficient depending on time and space variables under a final overdetermination condition. We obtain two types of conditions that are sufficient for the local solvability of the inverse problem and also prove the so-called Fredholm solvability of the inverse problem under study.

[1] Prilepko A. I., Solovev V. V., “Teoremy razreshimosti i metod Rote v obratnykh zadachakh dlya uravneniya parabolicheskogo tipa”, Differents. uravneniya, 23:11 (1987), 1971–1980 | MR | Zbl

[2] Solovev V. V., “O razreshimosti obratnoi zadachi opredeleniya istochnika s pereopredeleniem na verkhnei kryshke dlya parabolicheskogo uravneniya”, Differents. uravneniya, 25:9 (1989), 1577–1583 | MR | Zbl

[3] Kostin A. B., Prilepko A. I., “O razreshimosti obratnoi zadachi dlya uravneniya teploprovodnosti”, Obratnye zadachi dlya matematicheskikh modelei fizicheskikh protsessov, Sb. nauchnykh trudov, MIFI, M., 1991, 52–58

[4] Prilepko A. I., Kostin A. B., “O nekotorykh obratnykh zadachakh dlya parabolicheskikh uravnenii s finalnym i integralnym pereopredeleniem”, Matem. sb., 183:4 (1992), 49–68 | MR | Zbl

[5] Tkachenko D. S., “Ob odnoi obratnoi zadache dlya parabolicheskogo uravneniya s integralnym pereopredeleniem”, Algoritmicheskii analiz neustoichivykh zadach, Tezisy dokl. Vserossiiskoi nauchn. konferentsii, Izd-vo Uralskogo un-ta, Ekaterinburg, 2001, 120

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

[7] Alkhutov Yu. A., Mamedov I. T., “Pervaya kraevaya zadacha dlya nedivergentnykh parabolicheskikh uravnenii vtorogo poryadka s razryvnymi koeffitsientami”, Matem. sb., 173:12 (1986), 477–500

[8] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970

[9] Kruzhkov S. N., “Kvazilineinye parabolicheskie uravneniya i sistemy s dvumya nezavisimymi peremennymi”, Tr. sem. im. I. G. Petrovskogo, 5, Izd-vo Mosk. un-ta, M., 1979, 217–272 | MR | Zbl

[10] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz v normirovannykh prostranstvakh, Fizmatgiz, M., 1959