Projection method for the solution of a problem for a
Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 48-59.

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

This article investigates the boundary value problem for the quasilinear parabolic equation in noncylindrical domain. The existence and uniqueness are proved. The approximate solution built according to projection method. We use methods of compactness for functions from Banach space scale.
@article{DVMG_2012_12_1_a4,
     author = {K. V. Lisenkov},
     title = {Projection method for the solution of a problem for a},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {48--59},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2012},
     language = {ru},
     url = {https://geodesic-test.mathdoc.fr/item/DVMG_2012_12_1_a4/}
}
TY  - JOUR
AU  - K. V. Lisenkov
TI  - Projection method for the solution of a problem for a
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2012
SP  - 48
EP  - 59
VL  - 12
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DVMG_2012_12_1_a4/
LA  - ru
ID  - DVMG_2012_12_1_a4
ER  - 
%0 Journal Article
%A K. V. Lisenkov
%T Projection method for the solution of a problem for a
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2012
%P 48-59
%V 12
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DVMG_2012_12_1_a4/
%G ru
%F DVMG_2012_12_1_a4
K. V. Lisenkov. Projection method for the solution of a problem for a. Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 48-59. https://geodesic-test.mathdoc.fr/item/DVMG_2012_12_1_a4/

[1] N.E.Istomina, A.G.Podgaev, “O razreshimosti zadachi dlya kvazilineinogo vyrozhdayuschegosya parabolicheskogo uravneniya v oblasti s netsilindricheskoi granitsei”, Dalnevost. matem. zhurn., 1:1 (2000), 63–73

[2] P. V. Vinogradova, A. G. Zarubin, “O metode Galerkina dlya kvazilineinykh parabolicheskikh uravnenii v netsilindricheskoi oblasti”, Dalnevost. matem. zhurn., 3:1 (2002), 3–17

[3] J. Ferreira, N.A. Lar'kin, “Global solvability of a mixed problem for a nonlinear hyperbolic-parabolic equation in noncylindrical domains”, Portugaliae mathematica, 53:4 (1996), 381-395 | MR | Zbl

[4] S. N. Glazatov, “O nekotorykh zadachakh dlya dvazhdy nelineinykh parabolicheskikh uravnenii i uravnenii peremennogo tipa”, Matem. tr., 3:2 (2000), 71–110

[5] E. A. Baderko, “O razreshimosti granichnykh zadach dlya parabolicheskikh uravnenii vysokogo poryadka v oblastyakh s krivolineinymi bokovymi granitsami”, Differentsialnye uravneniya, 12:10 (1976), 1780–1792 | MR

[6] Yu. A. Dubinskii, “Nelineinye ellipticheskie i parabolicheskie uravneniya”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Nov. dostizh., 9, 1976, 1–130

[7] A. G. Podgaev, “Ob otnositelnoi kompaktnosti mnozhestva abstraktnykh funktsii iz shkaly banakhovykh prostranstv”, Sib. matem. zhurn., 34:2 (1993), 135–145

[8] Zh.L. Lions, Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972, 587 pp. | MR

[9] Ladyzhenskaya O.A., Solonnikov V.A., Uraltseva N.N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967, 736 pp. | MR