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

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Abstract

For the Vlasov-Maxwell system, sufficient conditions are obtained for the existence of bifurcation points λ0 ∈ℝ+ corresponding to distribution functions of the form

$$f_i (r, v) = \lambda \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{f} _i \left( { - \alpha _i v^2 + \varphi _i (r),vd_i + \psi _i (r)} \right)$$

.

It is assumed that the values of the scalar and vector potentials of the electromagnetic field are prescribed at the boundary of the domainD⊂ℝ3 in the form ρ|∂D =0,j|∂D=0, where ρ is the charge density andj 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.

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Authors and Affiliations

  1. Irkutsk State University, Irkutsk, USSR

    A. V. Sinitsyn

  2. Siberian Division of the Russian Academy of Sciences, Irkutsk Computer Center, USSR

    N. A. Sidorov

Authors
  1. N. A. Sidorov
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  2. A. V. Sinitsyn
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Translated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 268–292, August, 1997.

Translated by A. M. Chebotarev

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Sidorov, N.A., Sinitsyn, A.V. Analysis of bifurcation points and nontrivial branches of solutions to the stationary Vlasov-Maxwell system. Math Notes 62, 223–243 (1997). https://doi.org/10.1007/BF02355910

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