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Abstract <p>This work investigates an the inverse problem for the heat dissipation equation that has an additional higher order derivative in as an initial condition. In the beginning, it is considered the initial boundary value problem (direct problem). Theorem on a unique solvability of countable system of functional-integral equations is proved. The method of successive approximations is used in combination with the method of contraction mappings. The triple of solutions of the inverse problem is obtained in the form of Fourier series. Theorems on the existence and uniqueness of the solution to the problem are proved.</p>

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The Reverse Problem for the Heat Dissipation Equation That Has an Additional Higher Order Derivative in as an Initial Condition

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • O. Sh. Kilichov,
  • A. N. Ubaydulloev,
  • G. G. Qurbonov

摘要

Abstract

This work investigates an the inverse problem for the heat dissipation equation that has an additional higher order derivative in as an initial condition. In the beginning, it is considered the initial boundary value problem (direct problem). Theorem on a unique solvability of countable system of functional-integral equations is proved. The method of successive approximations is used in combination with the method of contraction mappings. The triple of solutions of the inverse problem is obtained in the form of Fourier series. Theorems on the existence and uniqueness of the solution to the problem are proved.