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We study the long-time asymptotic of the solutions to Maxwell's equation inthe case of a upper-hybrid resonance in the cold plasma model. We base ouranalysis in the transfer to the time domain of the recent results of B.Despr\'es, L.M. Imbert-G\'erard and R. Weder, J. Math. Pures Appl. {\bf 101} (2014) 623-659, where the singular solutions to Maxwell's equations in thefrequency domain were constructed by means of a limiting absorption principleand a formula for the heating of the plasma in the limit of vanishing collisionfrequency was obtained. Currently there is considerable interest in theseproblems, in particular, because upper-hybrid resonances are a possiblescenario for the heating of plasmas, and since they can be a model for thediagnostics involving wave scattering in plasmas.

Hybrid resonance and long-time asymptotic of the solution to Maxwell's equations