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 Mat. Zametki, 1997, Volume 62, Issue 2, Pages 268–292 (Mi mz1610)

Analysis of bifurcation points and nontrivial branches of solutions to the stationary Vlasov–Maxwell system

N. A. Sidorova, A. V. Sinitsynb

a Irkutsk State University
b Irkutsk Computer Centre, Siberian Branch of RAS

Abstract: For the Vlasov–Maxwell system, sufficient conditions are obtained for the existence of bifurcation points $\lambda _0\in \mathbb R^+$ corresponding to distribution functions of the form
$$f_i(r,v) =\lambda\widehat f_i(-\alpha_iv^2+\varphi_i(r), vd_i+\psi_i(r)).$$
It is assumed that the values of the scalar and vector potentials of the electromagnetic field are prescribed at the boundary of the domain $D\subset\mathbb R^3$ in the form $\rho|_{\partial D}=0$, $j|_{\partial D}=0$, where $\rho$ is the charge density and $j$ is the current density. The bifurcation equation is derived and studied for the solutions. The asymptotics of nontrivial solutions of the Vlasov–Maxwell system is constructed in a neighborhood of the bifurcation point.

DOI: https://doi.org/10.4213/mzm1610

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English version:
Mathematical Notes, 1997, 62:2, 223–243

Bibliographic databases:

UDC: 517.958+517.93

Citation: N. A. Sidorov, A. V. Sinitsyn, “Analysis of bifurcation points and nontrivial branches of solutions to the stationary Vlasov–Maxwell system”, Mat. Zametki, 62:2 (1997), 268–292; Math. Notes, 62:2 (1997), 223–243

Citation in format AMSBIB
\Bibitem{SidSin97} \by N.~A.~Sidorov, A.~V.~Sinitsyn \paper Analysis of bifurcation points and nontrivial branches of solutions to the stationary Vlasov--Maxwell system \jour Mat. Zametki \yr 1997 \vol 62 \issue 2 \pages 268--292 \mathnet{http://mi.mathnet.ru/mz1610} \crossref{https://doi.org/10.4213/mzm1610} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1619857} \zmath{https://zbmath.org/?q=an:0921.35010} \elib{http://elibrary.ru/item.asp?id=13250247} \transl \jour Math. Notes \yr 1997 \vol 62 \issue 2 \pages 223--243 \crossref{https://doi.org/10.1007/BF02355910} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000071268600029} 

• http://mi.mathnet.ru/eng/mz1610
• https://doi.org/10.4213/mzm1610
• http://mi.mathnet.ru/eng/mz/v62/i2/p268

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

This publication is cited in the following articles:
1. N. A. Sidorov, V. R. Abdullin, “Interlaced branching equations in the theory of non-linear equations”, Sb. Math., 192:7 (2001), 1035–1052
2. N. A. Sidorov, R. Yu. Leontiev, A. I. Dreglea, “On Small Solutions of Nonlinear Equations with Vector Parameter in Sectorial Neighborhoods”, Math. Notes, 91:1 (2012), 90–104
3. N. A. Sidorov, “Bifurcation points of nonlinear operators: existence theorems, asymptotics and application to the Vlasov–Maxwell system”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 6:4 (2013), 85–106
4. A. L. Skubachevskii, “Vlasov–Poisson equations for a two-component plasma in a homogeneous magnetic field”, Russian Math. Surveys, 69:2 (2014), 291–330
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