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The Cauchy Problem for One Equation of Sobolev Type

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Abstract

We give necessary and sufficient conditions for the existence of a solution to the Cauchy problem for the equation Δk∂ 2 t u + (−1)ku = 0 in the space of tempered distributions.

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Authors and Affiliations

  1. Donetsk National University, Donetsk, 283001, Ukraine

    A. L. Pavlov

  2. Insititute of Applied Mathematics and Mechanics, Donetsk, 283114, Ukraine

    A. L. Pavlov

Authors
  1. A. L. Pavlov
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Correspondence to A. L. Pavlov.

Additional information

Russian Text © A.L. Pavlov, 2018, published in Matematicheskie Trudy, 2018, Vol. 21, No. 1, pp. 125–154.

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Pavlov, A.L. The Cauchy Problem for One Equation of Sobolev Type. Sib. Adv. Math. 29, 57–76 (2019). https://doi.org/10.3103/S105513441901005X

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  • DOI: https://doi.org/10.3103/S105513441901005X

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