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The Kovalevskaya theorem and the modern theory of partial differential equations. (Russian. English summary) Zbl 0880.35007
The author gives the historic background of the Cauchy-Kovalevskaya theorem, describes basic ideas of its proof, and discusses generalizations of this theorem obtained by J. Leray, S. Mizohata, and L. Hörmander, as well as related results by H. Lewy, Yu. V. Egorov, and other authors including a theorem by J.-M. Bony and P. Schapira [Asterisque 2/3, 108-116 (1973; Zbl 0289.35016)]. The paper is based on a lecture given by the author for secondary school teachers in the framework of the “International Soros Science Educational Program” and is aimed at presenting contemporary developments in mathematics on an elementary level understandable for secondary school teachers and pupils.
MSC:
35A10 Cauchy-Kovalevskaya theorems
00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)
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