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Elenbaas problem of electric arc discharge. / Pavlenko, V.N.; Potapov, D.K.

In: Mathematical Notes, Vol. 103, No. 1-2, 01.01.2018, p. 89-95.

Research output: Contribution to journal › Article › peer-review

Harvard

Pavlenko, VN & Potapov, DK 2018, 'Elenbaas problem of electric arc discharge', Mathematical Notes, vol. 103, no. 1-2, pp. 89-95. https://doi.org/10.1134/S0001434618010108

APA

Pavlenko, V. N., & Potapov, D. K. (2018). Elenbaas problem of electric arc discharge. Mathematical Notes, 103(1-2), 89-95. https://doi.org/10.1134/S0001434618010108

Vancouver

Pavlenko VN, Potapov DK. Elenbaas problem of electric arc discharge. Mathematical Notes. 2018 Jan 1;103(1-2):89-95. https://doi.org/10.1134/S0001434618010108

Author

Pavlenko, V.N. ; Potapov, D.K. / Elenbaas problem of electric arc discharge. In: Mathematical Notes. 2018 ; Vol. 103, No. 1-2. pp. 89-95.

BibTeX

@article{25902d20a4f5447f81e8fa2d3cdb1490,
title = "Elenbaas problem of electric arc discharge",
abstract = "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 λmin of the values of the parameter λ for which the electric discharge is possible is obtained. The fact that the discharge domain appears for any λ ≥ λ 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 = "discontinuous nonlinearity, electric arc, Elenbaas problem, free boundary",
author = "V.N. Pavlenko and D.K. Potapov",
year = "2018",
month = jan,
day = "1",
doi = "10.1134/S0001434618010108",
language = "English",
volume = "103",
pages = "89--95",
journal = "Mathematical Notes",
issn = "0001-4346",
publisher = "Pleiades Publishing",
number = "1-2",

}

RIS

TY - JOUR

T1 - Elenbaas problem of electric arc discharge

AU - Pavlenko, V.N.

AU - Potapov, D.K.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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 λmin of the values of the parameter λ for which the electric discharge is possible is obtained. The fact that the discharge domain appears for any λ ≥ λ 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.

AB - 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 λmin of the values of the parameter λ for which the electric discharge is possible is obtained. The fact that the discharge domain appears for any λ ≥ λ 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.

KW - discontinuous nonlinearity

KW - electric arc

KW - Elenbaas problem

KW - free boundary

UR - http://www.scopus.com/inward/record.url?scp=85043763411&partnerID=8YFLogxK

U2 - 10.1134/S0001434618010108

DO - 10.1134/S0001434618010108

M3 - Article

VL - 103

SP - 89

EP - 95

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 1-2

ER -

ID: 32592898