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

This article is cited in 4 scientific papers (total in 4 papers)

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
Received: 08.09.1995

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
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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    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  mathnet
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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