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Abstract <p>For a one-dimensional boundary problem associated with a linear parabolic equation in the presence of a nonlocal spatial condition, necessary and sufficient conditions for the existence of a solution are established. Structural proof of the existence of a solution is presented. By means of Laguerre polynomials, a solution is explicitly constructed in the form of a functional series.</p>

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Solution of a One-Dimensional Parabolic Problem with a Nonlocal Boundary Condition

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • I. A. Danilina,
  • Yu. A. Kostikov,
  • A. M. Romanenkov

摘要

Abstract

For a one-dimensional boundary problem associated with a linear parabolic equation in the presence of a nonlocal spatial condition, necessary and sufficient conditions for the existence of a solution are established. Structural proof of the existence of a solution is presented. By means of Laguerre polynomials, a solution is explicitly constructed in the form of a functional series.