Abstract
The investigations ofRosenbloom-Widder [13] on expansions in terms of heat polynomials have been generalized for partial differential equations of second order with singular coefficients, equations of higher order etc. In the present paper we introduce a new method for the discussion of such problems. The technique is related to the treatment of the Cauchy problem on the base of the Ovcyannikov theorem. The method is used for the discussion of two classes of partial differential equations of arbitrary order.
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