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

N. A. Sidorov ; A. V. Sinitsyn

Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 268-292

Résumé

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 $$ f_i(r,v) =\lambda\widehat f_i\bigl(-\alpha_iv^2+\varphi_i(r), vd_i+\psi_i(r)\bigr). $$ 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.