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Necessary and Sufficient Conditions for the Solvability of the Complex Cauchy Problem in Classes of Functions of Vector-Exponential Type

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Abstract

We consider the Cauchy problem for general linear systems of complex partial differential equations in scales of Banach spaces of vector functions of the exponential type with an integral metric. Necessary and sufficient conditions for the well-posed solvability of this problem are obtained. Thus, we describe the structure of linear systems of complex partial differential equations for which the Cauchy problem is well posed.

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Funding

This work was supported by the Russian Science Foundation, project no. 19-11-00033.

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Authors and Affiliations

  1. National Research University “Moscow Power Engineering Institute”, Moscow, 111250, Russia

    A. M. Biryukov

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  1. A. M. Biryukov
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Correspondence to A. M. Biryukov.

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Translated by V. Potapchouck

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Biryukov, A.M. Necessary and Sufficient Conditions for the Solvability of the Complex Cauchy Problem in Classes of Functions of Vector-Exponential Type. Diff Equat 56, 1031–1040 (2020). https://doi.org/10.1134/S0012266120080066

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  • DOI: https://doi.org/10.1134/S0012266120080066

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