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Neumann problem with the integro-differential operator in the boundary condition

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Abstract

The Neumann problem for a second-order parabolic equation with integro-differential operator in the boundary condition is considered. A well-posedness theorem is proved, in particular, the integral representation of the solution is obtained, estimates for the derivatives of the solution are established, and the kernel of the inverse operator of the problem is explicitly expressed.

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Authors and Affiliations

  1. Fedkovych Chernivtsi National University, Chernivtsi, Ukraine

    I. M. Danyliuk

  2. Bukovyna State University of Finance and Economics, Chernivtsi, Ukraine

    A. O. Danyliuk

Authors
  1. I. M. Danyliuk
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  2. A. O. Danyliuk
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Correspondence to I. M. Danyliuk.

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Original Russian Text © I. M. Danyliuk, A. O. Danyliuk, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 5, pp. 701–709.

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Danyliuk, I.M., Danyliuk, A.O. Neumann problem with the integro-differential operator in the boundary condition. Math Notes 100, 687–694 (2016). https://doi.org/10.1134/S0001434616110055

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