Abstract.
The paper is devoted to the presentation of Leray’s approach to the Cauchy problem for strictly hyperbolic operators. In the first section we give the main definitions of strictly hyperbolic operators and separating operators corresponding to them. We present the plan of derivation of the a priori estimates necessary for the proof of solvability of the Cauchy problem. In the second section we generalize the Leray approach to some classes of PDO which are not hyperbolic.
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Volevich, L.R. The Leray separating operator in the theory of the Cauchy problem. J.fixed point theory appl. 1, 293–304 (2007). https://doi.org/10.1007/s11784-007-0015-8
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DOI: https://doi.org/10.1007/s11784-007-0015-8