Geodesic
Singular Perturbations of Non-Linear Elliptic and Parabolic Variational Boundary-Value Problems
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 861-872

Voir la notice de l'article provenant de la source Cambridge University Press

Singular perturbations of linear elliptic and parabolic boundary-value problems have been studied extensively by Visik and Lyusternik (7), Huet (5), and others. It is the purpose of this paper to extend the results of (5) to the non-linear elliptic and parabolic variational boundary-value problems considered during the last few years by Browder (2, 4).In §1, we give the notations and state the main assumptions on the nonlinearity of the elliptic operators. In §2 we study the singular perturbations of non-linear elliptic variational boundary problems. In §3, we consider the case of non-linear parabolic variational boundary problems with a small parameter. 
Ton, Bui An. Singular Perturbations of Non-Linear Elliptic and Parabolic Variational Boundary-Value Problems. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 861-872. doi: 10.4153/CJM-1966-086-2
@article{10_4153_CJM_1966_086_2,
     author = {Ton, Bui An},
     title = {Singular {Perturbations} of {Non-Linear} {Elliptic} and {Parabolic} {Variational} {Boundary-Value} {Problems}},
     journal = {Canadian journal of mathematics},
     pages = {861--872},
     year = {1966},
     volume = {18},
     number = {1},
     doi = {10.4153/CJM-1966-086-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-086-2/}
}
TY  - JOUR
AU  - Ton, Bui An
TI  - Singular Perturbations of Non-Linear Elliptic and Parabolic Variational Boundary-Value Problems
JO  - Canadian journal of mathematics
PY  - 1966
SP  - 861
EP  - 872
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-086-2/
DO  - 10.4153/CJM-1966-086-2
ID  - 10_4153_CJM_1966_086_2
ER  - 
%0 Journal Article
%A Ton, Bui An
%T Singular Perturbations of Non-Linear Elliptic and Parabolic Variational Boundary-Value Problems
%J Canadian journal of mathematics
%D 1966
%P 861-872
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-086-2/
%R 10.4153/CJM-1966-086-2
%F 10_4153_CJM_1966_086_2

[1] 1. Aubin, J. P., Un théorème de compacité, C. R. Acad. Sci., Paris, 256 (1963), 5042–5044. Google Scholar

[2] 2. Browder, F. E., Variational boundary value problems for quasi linear elliptic equations of arbitrary order, Proc. Nat. Acad. Sci. U.S.A., 50 (1963), 31–37. Google Scholar

[3] 3. Browder, F. E., Variational boundary value problems for quasi linear elliptic equations II, Proc. Nat. Acad. Sci. U.S.A., 50 (1963), 592–598. Google Scholar

[4] 4. Browder, F. E., Strongly non-linear parabolic boundary value problems, Amer. J. Math., 86 (1964), 339–357. Google Scholar

[5] 5. Huet, D., Phénomènes de perturbations singulières, Ann. Inst. Fourier, Grenoble, 10 (1960), 1–96. Google Scholar

[6] 6. Ton, B. A., Elliptic boundary problems with a small parameter, J. Math. Anal. Appl., 4 (1966). Google Scholar

[7] 7. Visik, M. I. and Luysternik, L. A., Regular degeneration and boundary layer for linear differential equations with a small parameter, Uspehi Mat. Nauk (N.S.), 12 (1957), 3–122 = Amer. Math. Soc. Transi. Ser. 2, 20 (1962), 239-364. Google Scholar

Cité par Sources :