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An existence and uniqueness theorem for the Vlasov-Maxwell system. (English) Zbl 0592.45010

The purpose of the present paper is to give a local existence and uniqueness theorem for the Vlasov-Maxwell system of equations, which is one of the fundamental sets of equations underlying the kinetic theory of plasma. It is a nonlinear integro-differential system which describes the collective motion of charged particles in the presence of their own self- generated electromagnetic field.

MSC:

45K05 Integro-partial differential equations
78A35 Motion of charged particles
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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References:

[1] Cooper, J. Math. Anal. Appl. 75 pp 306– (1980)
[2] Duniec, Bull. Acad. Polar. Sci. Ser. Sci. Tech. 21 pp 97– (1973)
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[4] Neunzert, Math. Meth. in the Appl. Sci. 2 pp 429– (1980)
[5] Existence and uniqueness theory of the Vlasov equation, Technical Report MF-100, Magneto-Fluid Dynamics Division, Courant Institute, New York University, 1982.
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