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