Geodesic
Boundary value problems for systems of equations of two-phase porous flow type; statement of the problems, questions of solvability, justification of approximate methods
Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 62-80
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A system of two second order quasilinear equations (one elliptic and one parabolic) is investigated. Such a system is formed by the equations of two-phase porous flow. Boundary value problems are considered for the system, and existence, uniqueness, and stability theorems are proved for the solutions of the problems in the nondegenerate plane case. A justification is given for some approximate methods of constructing the solutions. Bibliography: 10 titles. 
@article{SM_1977_33_1_a4,
     author = {S. N. Kruzhkov and S. M. Sukoryanskii},
     title = {Boundary value problems for systems of equations of two-phase porous flow type; statement of the problems, questions of solvability, justification of approximate methods},
     journal = {Sbornik. Mathematics},
     pages = {62--80},
     year = {1977},
     volume = {33},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_33_1_a4/}
}
TY  - JOUR
AU  - S. N. Kruzhkov
AU  - S. M. Sukoryanskii
TI  - Boundary value problems for systems of equations of two-phase porous flow type; statement of the problems, questions of solvability, justification of approximate methods
JO  - Sbornik. Mathematics
PY  - 1977
SP  - 62
EP  - 80
VL  - 33
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1977_33_1_a4/
LA  - en
ID  - SM_1977_33_1_a4
ER  - 
%0 Journal Article
%A S. N. Kruzhkov
%A S. M. Sukoryanskii
%T Boundary value problems for systems of equations of two-phase porous flow type; statement of the problems, questions of solvability, justification of approximate methods
%J Sbornik. Mathematics
%D 1977
%P 62-80
%V 33
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1977_33_1_a4/
%G en
%F SM_1977_33_1_a4
S. N. Kruzhkov; S. M. Sukoryanskii. Boundary value problems for systems of equations of two-phase porous flow type; statement of the problems, questions of solvability, justification of approximate methods. Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 62-80. http://geodesic.mathdoc.fr/item/SM_1977_33_1_a4/

[1] Ya. Ber, D. Zaslavski, S. Irmei, Fiziko-matematicheskie osnovy filtratsii vody, izd-vo «Mir», Moskva, 1971

[2] M. Leverett, “Capillary behaviour in porous solids”, Trans. AIME, 142 (1941), 151

[3] S. N. Antontsev, “O razreshimosti kraevykh zadach dlya vyrozhdayuschikhsya uravnenii dvukhfaznoi filtratsii”, Dinamika sploshnoi sredy, no. 10, izd-vo in-ta gidrodinamiki SO AN SSSR, Novosibirsk, 1972, 28–53

[4] M. I. Shvidler, B. I. Levi, Odnomernaya filtratsiya nesmeshivayuschikhsya zhidkostei, izd-vo «Nedra», Moskva, 1970

[5] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, izd-vo «Nauka», Moskva, 1973 | MR

[6] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, izd-vo «Nauka», Moskva, 1967

[7] L. V. Kantorovich, G. P. Akilov, Funktsionalnyi analiz v normirovannykh prostranstvakh, Fizmatgiz, Moskva, 1959 | MR

[8] S. Agmon, A. Duglis, L. Nirenberg, Otsenki reshenii ellipticheskikh uravnenii vblizi granitsy, IL, Moskva, 1962

[9] S. A. Arakcheev, “O gladkosti obobschennykh reshenii nekorogo klassa kvazilineinykh ellipticheskikh uravnenii”, Vestnik MGU, seriya matem., mekhan., 1975, no. 1, 49–57 | Zbl

[10] I. N. Vekua, Obobschennye analiticheskie funktsii, Fizmatgiz, Moskva, 1959 | MR