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arXiv · 1608.05599

A criterion of solvability of the elliptic Cauchy problem in a multi-dimensional cylindrical domain

Tynysbek Sh. Kalmenov·Makhmud A. Sadybekov·Berikbol T. Torebek
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Abstract

In this paper we consider the Cauchy problem for multidimensional elliptic equations in a cylindrical domain. The method of spectral expansion in eigenfunctions of the Cauchy problem for equations with deviating argument establishes a criterion of the strong solvability of the considered elliptic Cauchy problem. It is shown that the ill-posedness of the elliptic Cauchy problem is equivalent to the existence of an isolated point of the continuous spectrum for a self-adjoint operator with deviating argument.

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Tynysbek Sh. Kalmenov, Makhmud A. Sadybekov, Berikbol T. Torebek. 2016-08-19. A criterion of solvability of the elliptic Cauchy problem in a multi-dimensional cylindrical domain. https://doi.org/10.1080/17476933.2018.1437423

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