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Boundary-value problems for a hyperbolic equation with nonlocal conditions of the I and II kind

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Abstract

In this paper we consider two initial-boundary value problems with nonlocal conditions. The main goal is to propose a method for proving the solvability of nonlocal problems with integral conditions of the first kind. The proposed method is based on the equivalence of a nonlocal problem with an integral condition of the first kind and a nonlocal problem with an integral condition of the second kind in a special form. We prove the unique existence of generalized solutions to both problems.

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Authors and Affiliations

  1. Samara State University, ul. Akad. Pavlova 1, Samara, 443011, Russia

    L. S. Pul’kina

Authors
  1. L. S. Pul’kina
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Correspondence to L. S. Pul’kina.

Additional information

Original Russian Text © L.S. Pul’kina, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 4, pp. 74–83.

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Pul’kina, L.S. Boundary-value problems for a hyperbolic equation with nonlocal conditions of the I and II kind. Russ Math. 56, 62–69 (2012). https://doi.org/10.3103/S1066369X12040081

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  • DOI: https://doi.org/10.3103/S1066369X12040081

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