Geodesic
Progective algorithm of boundary value problem for inhomogeneous Lame's equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 236-240.

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

The method of boundary value problem solution for the stationary inhomogeneous Lame's equation is considered. An appointed vector-function space splitting is used that leads to inhomogeneous biharmonic equation and Poisson's equation problems for components of required vector field. The basic potentials method is proposed to solve these problems.
Mots-clés : Lame's equation
Keywords: Weyl's expansion, bigarmonic equation, basic potentials method (of fundamental solutions). 
@article{VSGTU_2011_1_a29,
     author = {V. G. Lezhnev and A. N. Markovsky},
     title = {Progective algorithm of boundary value problem for inhomogeneous {Lame's} equation},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {236--240},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a29/}
}
TY  - JOUR
AU  - V. G. Lezhnev
AU  - A. N. Markovsky
TI  - Progective algorithm of boundary value problem for inhomogeneous Lame's equation
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2011
SP  - 236
EP  - 240
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a29/
LA  - ru
ID  - VSGTU_2011_1_a29
ER  - 
%0 Journal Article
%A V. G. Lezhnev
%A A. N. Markovsky
%T Progective algorithm of boundary value problem for inhomogeneous Lame's equation
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2011
%P 236-240
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a29/
%G ru
%F VSGTU_2011_1_a29
V. G. Lezhnev; A. N. Markovsky. Progective algorithm of boundary value problem for inhomogeneous Lame's equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 236-240. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a29/

[1] Oleynik O. A., Iosif'yan G. A., Shamaev A. S., Mathematical problems in the theory of strongly inhomogeneous elastic media, MGU, Moscow, 1990, 312 pp. | MR

[2] Bykhovskiy É. B., Smirnov N. V., “Orthogonal decomposition of the space of vector functions square-summable on a given domain, and the operators of vector analysis”, Mathematical problems of hydrodynamics and magnetohydrodynamics for a viscous incompressible fluid, Collected papers, Trudy Mat. Inst. Steklov., 59, Acad. Sci. USSR, Moscow–Leningrad, 1960, 5–36 | MR

[3] Ladyzhenskaya O. A., Mathematical questions of the dynamics of a viscous incompressible fluid, Nauka, Moscow, 1970, 288 pp. | MR

[4] Lezhnev A. V, Lezhnev V. G., Method of basic potentials in problems of mathematical physics and hydrodynamics, KubGU, Krasnodar, 2009, 111 pp.

[5] Lezhnev V. G., Markovskiy A. N., “Method of basis potentials for inhomogeneous biharmonic equation”, Vestn. Samar. Gos. Univ. Estestvennonauchn. Ser., 2008, no. 8/1(67), 127–139

[6] Nazarov S. A., Specovius-Neugebauer M., “Approximation of unbounded domains by bounded domains. Boundary value problems for the Lamé operator”, St. Petersburg Math. J., 8:5 (1997), 879–912 | MR