V. N. Pavlenko, D. K. Potapov, “Elenbaas Problem of Electric Arc Discharge”, Mat. Zametki, 103:1 (2018), 92–100; Math. Notes, 103:1 (2018), 89

Loading [MathJax]/jax/element/mml/optable/SuppMathOperators.js

Matematicheskie Zametki

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mat. Zametki:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Matematicheskie Zametki, 2018, Volume 103, Issue 1, Pages 92–100
DOI: https://doi.org/10.4213/mzm11280 (Mi mzm11280)

This article is cited in 7 scientific papers (total in 7 papers)

Elenbaas Problem of Electric Arc Discharge

V. N. Pavlenko^a, D. K. Potapov^b

^a Chelyabinsk State University
^b Saint Petersburg State University

Full-text PDF (471 kB) Citations (7)

References:

PDF

HTML

DOI: https://doi.org/10.4213/mzm11280

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

$\lambda_{\min}$ 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.

Received: 30.05.2016
Revised: 03.11.2016

English version:
Mathematical Notes, 2018, Volume 103, Issue 1, Pages 89–95
DOI: https://doi.org/10.1134/S0001434618010108

Bibliographic databases:

Document Type: Article

UDC: 517.958

Language: Russian

Citation: V. N. Pavlenko, D. K. Potapov, “Elenbaas Problem of Electric Arc Discharge”, Mat. Zametki, 103:1 (2018), 92–100; Math. Notes, 103:1 (2018), 89–95

Citation in format AMSBIB

\Bibitem{PavPot18}

\by V.~N.~Pavlenko, D.~K.~Potapov

\paper Elenbaas Problem of Electric Arc Discharge

\jour Mat. Zametki

\yr 2018

\vol 103

\issue 1

\pages 92--100

\mathnet{http://mi.mathnet.ru/mzm11280}

\crossref{https://doi.org/10.4213/mzm11280}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3740288}

\elib{https://elibrary.ru/item.asp?id=30762110}

\transl

\jour Math. Notes

\yr 2018

\vol 103

\issue 1

\pages 89--95

\crossref{https://doi.org/10.1134/S0001434618010108}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000427616800010}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85043763411}

Linking options:

https://www.mathnet.ru/eng/mzm11280

https://doi.org/10.4213/mzm11280

https://www.mathnet.ru/eng/mzm/v103/i1/p92

This publication is cited in the following 7 articles:

J. A. Santos, P. F. S. Pontes, S. H. M. Soares, “A global result for a degenerate quasilinear eigenvalue problem with discontinuous nonlinearities”, Calc. Var., 62:3 (2023)
N. Nefedov, B. Tishchenko, N. Levashova, “An algorithm for construction of the asymptotic approximation of a stable stationary solution to a diffusion equation system with a discontinuous source function”, Algorithms, 16:8 (2023), 359
V. N. Pavlenko, D. K. Potapov, “One class of quasilinear elliptic type equations with discontinuous nonlinearities”, Izv. Math., 86:6 (2022), 1162–1178
V. N. Pavlenko, D. K. Potapov, “Positive solutions of superlinear elliptic problems with discontinuous non-linearities”, Izv. Math., 85:2 (2021), 262–278
V. N. Pavlenko, D. K. Potapov, “Variational method for elliptic systems with discontinuous nonlinearities”, Sb. Math., 212:5 (2021), 726–744
V. N. Pavlenko, D. K. Potapov, “On a class of elliptic boundary-value problems with parameter and discontinuous non-linearity”, Izv. Math., 84:3 (2020), 592–607
V. N. Pavlenko, D. K. Potapov, “Properties of the spectrum of an elliptic boundary value problem with a parameter and a discontinuous nonlinearity”, Sb. Math., 210:7 (2019), 1043–1066

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	478
Full-text PDF :	55
References:	82
First page:	26

Что такое QR-код?

Registration to the website

Logotypes