Geodesic
Elenbaas Problem of Electric Arc Discharge
Matematičeskie zametki, Tome 103 (2018) no. 1, pp. 92-100

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

The Elenbaas problem of electric discharge origination is considered. The mathematical model is an elliptic boundary-value problem with a parameter and discontinuous nonlinearity. The nontrivial solutions of the problem determine the free boundaries separating different phase states. A survey of results obtained for this problem is given. The greatest lower bound $\lambda_{\min}$ of the values of the parameter $\lambda$ for which the electric discharge is possible is obtained. The fact that the discharge domain appears for any $\lambda \ge \lambda_{\min}$ is proved. The range of the parameter values for which the boundary of the discharge domain is of two-dimensional Lebesgue measure zero is determined. An unsolved problem is formulated.
Keywords: Elenbaas problem, electric arc, free boundary, discontinuous nonlinearity. 
@article{MZM_2018_103_1_a7,
     author = {V. N. Pavlenko and D. K. Potapov},
     title = {Elenbaas {Problem} of {Electric} {Arc} {Discharge}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {92--100},
     publisher = {mathdoc},
     volume = {103},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_1_a7/}
}
TY  - JOUR
AU  - V. N. Pavlenko
AU  - D. K. Potapov
TI  - Elenbaas Problem of Electric Arc Discharge
JO  - Matematičeskie zametki
PY  - 2018
SP  - 92
EP  - 100
VL  - 103
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_103_1_a7/
LA  - ru
ID  - MZM_2018_103_1_a7
ER  - 
%0 Journal Article
%A V. N. Pavlenko
%A D. K. Potapov
%T Elenbaas Problem of Electric Arc Discharge
%J Matematičeskie zametki
%D 2018
%P 92-100
%V 103
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_103_1_a7/
%G ru
%F MZM_2018_103_1_a7
V. N. Pavlenko; D. K. Potapov. Elenbaas Problem of Electric Arc Discharge. Matematičeskie zametki, Tome 103 (2018) no. 1, pp. 92-100. http://geodesic.mathdoc.fr/item/MZM_2018_103_1_a7/