Abstract
An initial-boundary value problem for the multidimensional equation of ion-sound waves in a plasma is considered. Its time-local solvability in the classical sense in Holder spaces is proved. This is a development of results in our previous papers, where the local solvability of one-dimensional analogs of the equation under consideration was established and, in the general case (regardless of the dimension of the space), sufficient conditions for the blow-up of the solution were obtained.
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