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Well-posed solvability of an analytic Cauchy problem in spaces with an integral metric

  • Partial Differential Equations
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Abstract

We study the complex Cauchy problem for a system of linear differential equations in a class of analytic functions with an integral metric. For the case in which L p is a weighted Lebesgue space, we obtain necessary and sufficient conditions for the local solvability of the problem.

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References

  1. Dubinskii, Yu.A., Zadacha Koshi v kompleksnoi oblasti (Cauchy Problem in the Complex Domain), Moscow, 1996.

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  2. Biryukov, A.M., Complex Cauchy Problem in the Class of Analytic Functions with Integral Metric, Differ. Uravn., 2013, vol. 49, no. 6, pp. 779–783.

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  4. Biryukov, A.M., Complex Cauchy Problem in Spaces with Integral Metrics, Vestn. Moskov. Energ. Inst., 2011, no. 6, pp. 126–132.

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Authors and Affiliations

  1. National Research University “Moscow Power Engineering Institute,”, Moscow, 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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Original Russian Text © A.M. Biryukov, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 4, pp. 470–480.

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Biryukov, A.M. Well-posed solvability of an analytic Cauchy problem in spaces with an integral metric. Diff Equat 52, 447–457 (2016). https://doi.org/10.1134/S0012266116040054

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  • DOI: https://doi.org/10.1134/S0012266116040054

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