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Integral Analogue of the First Initial-Boundary Value Problem for Second-Order Hyperbolic and Parabolic Equations

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Abstract

We study the solvability of initial-boundary value problems for second-order hyperbolic and parabolic equations with a boundary condition that integrally connects the values of the solution on the lateral boundary with the values of the solution inside the domain. To study such problems, it was previously established that their solvability is ensured by the bijectivity of a certain Fredholm operator constructed from an integral condition. In this paper, we show that the condition of predecessors is not required for the existence and uniqueness of regular solutions (solutions with all derivatives generalized in the sense of Sobolev that are contained in the equation) of integral analogues of the first initial-boundary value problem for second-order hyperbolic and parabolic equations.

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Funding

This work was carried out for the Federal Target Program “Program of Fundamental Research at SamSTU in the Field of Chemical Sciences and Material Science”, grant no. FSSE-2020-0005.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090, Russia

    A. I. Kozhanov

  2. Samara State Technical University, Samara, 443100, Russia

    A. I. Kozhanov & A. V. Dyuzheva

Authors
  1. A. I. Kozhanov
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  2. A. V. Dyuzheva
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Corresponding author

Correspondence to A. I. Kozhanov.

Additional information

Translated from Matematicheskie Zametki, 2022, Vol. 111, pp. 540-550 https://doi.org/10.4213/mzm13326.

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Kozhanov, A.I., Dyuzheva, A.V. Integral Analogue of the First Initial-Boundary Value Problem for Second-Order Hyperbolic and Parabolic Equations. Math Notes 111, 562–570 (2022). https://doi.org/10.1134/S0001434622030245

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  • DOI: https://doi.org/10.1134/S0001434622030245

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