Geodesic
Asymptotics of a boundary-value problem solution for the Laplace equation with type changing of the boundary condition on two small sites
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 3, pp. 266-281

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

We consider a harmonic function in a three-dimensional bounded domain. The normal derivative is given on almost the entire boundary, excepting two small sections, on which the value of the function itself is specified. For such a harmonic function, by the method of matching asymptotic expansions, a two-scale asymptotics with respect to a small parameter characterizing the size of the mentioned boundary sections is constructed and justified. The physical application of the obtained decomposition is given.
Keywords: boundary value problem, Laplace equation, asymptotic expansion, mixed problem, small parameter, matching method, electrical resistance. 
@article{CHFMJ_2017_2_3_a1,
     author = {A. A. Ershov and M. I. Rusanova},
     title = {Asymptotics of a  boundary-value problem solution for the {Laplace} equation with type changing of the boundary condition on two small sites},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {266--281},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a1/}
}
TY  - JOUR
AU  - A. A. Ershov
AU  - M. I. Rusanova
TI  - Asymptotics of a  boundary-value problem solution for the Laplace equation with type changing of the boundary condition on two small sites
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2017
SP  - 266
EP  - 281
VL  - 2
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a1/
LA  - ru
ID  - CHFMJ_2017_2_3_a1
ER  - 
%0 Journal Article
%A A. A. Ershov
%A M. I. Rusanova
%T Asymptotics of a  boundary-value problem solution for the Laplace equation with type changing of the boundary condition on two small sites
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2017
%P 266-281
%V 2
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a1/
%G ru
%F CHFMJ_2017_2_3_a1
A. A. Ershov; M. I. Rusanova. Asymptotics of a  boundary-value problem solution for the Laplace equation with type changing of the boundary condition on two small sites. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 3, pp. 266-281. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a1/