On approximate methods of solving nonlinear boundary value problems with a small parameter
Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 491-500 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Variational inequalities with a small parameter are considered, together with closely related nonlinear operator equations. The penalty method as applied to variational inequalities is studied, and Galerkin's method relative to nonlinear equations. Under conditions of monotonicity, coerciveness and hemicontinuity on the operators, uniform convergence (with respect to the small parameter) of the approximate solutions thus obtained to the exact solution is demonstrated. Bibliography: 12 titles.
@article{SM_1976_28_4_a3,
     author = {L. A. Kalyakin},
     title = {On approximate methods of solving nonlinear boundary value problems with a~small parameter},
     journal = {Sbornik. Mathematics},
     pages = {491--500},
     year = {1976},
     volume = {28},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_28_4_a3/}
}
TY  - JOUR
AU  - L. A. Kalyakin
TI  - On approximate methods of solving nonlinear boundary value problems with a small parameter
JO  - Sbornik. Mathematics
PY  - 1976
SP  - 491
EP  - 500
VL  - 28
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1976_28_4_a3/
LA  - en
ID  - SM_1976_28_4_a3
ER  - 
%0 Journal Article
%A L. A. Kalyakin
%T On approximate methods of solving nonlinear boundary value problems with a small parameter
%J Sbornik. Mathematics
%D 1976
%P 491-500
%V 28
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1976_28_4_a3/
%G en
%F SM_1976_28_4_a3
L. A. Kalyakin. On approximate methods of solving nonlinear boundary value problems with a small parameter. Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 491-500. http://geodesic.mathdoc.fr/item/SM_1976_28_4_a3/

[1] M. I. Vishik, L. A. Lyusternik, “Regulyarnoe vyrozhdenie i pogranichnyi sloi dlya lineinykh differentsialnykh uravnenii s malym parametrom”, Uspekhi matem. nauk, XII:5 (77) (1957), 3–120 | MR

[2] J.-L. Lions, Perturbations singulières dams les problèmes aux limites et en controle optimal, Lect. Notes Math., 323, Springer-Verlag, Berlin, 1973 | MR | Zbl

[3] A. M. Ilin, “Raznostnaya skhema dlya differentsialnogo uravneniya s malym parametrom pri starshei proizvodnoi”, Matem. zametki, 6:2 (1969), 237–248 | MR

[4] K. E. Barrett, “The numerical solution of singular perturbation boundary-value problems”, Quart. J. Mech. and Appl. Math., 27:1 (1974), 57–68 | DOI | MR | Zbl

[5] K. V. Emelyanov, “Raznostnaya skhema dlya trekhmernogo ellipticheskogo uravneniya s malym parametrom pri starshikh proizvodnykh”, Kraevye zadachi dlya uravnenii matem. fiziki, UNTs AN SSSR, Sverdlovsk, 1973, 30–42

[6] L. A. Kalyakin, “Metod Rittsa dlya uravnenii s malym parametrom pri starshikh proizvodnykh”, Matem. zametki, 6:1 (1969), 91–96

[7] L. A. Kalyakin, “Metod Galerkina dlya uravnenii s malym parametrom pri starshikh proizvodnykh”, Matem. sb., 85 (127) (1971), 527–537

[8] D. Huet, “Perturbations singulières d'inéqalités variationelles”, C. r. Acad. scient. Paris, 267 (1968), 932–934 | MR

[9] J.-L. Lions, “Sur les perturbations singulières et les développements asymptotiques dans les inequations aux derivées partielles”, C. r. Acad. scient. Paris, 272 (1971) | MR | Zbl

[10] D. Huet, “Singular perturbations of elliptic problems”, Ann. mat. pura ed appl., XCV (1973), 77–114 | DOI | MR

[11] Zh.-L. Lions, Nekotorye metody resheniya nelineinykh kraevykh zadach, izd-vo «Mir», Moskva, 1972 | MR

[12] J. Singer, “Some remarks on approximative compactness”, Rev. roumaine Math. pures et appl., 9:2 (1964), 167–177 | MR | Zbl