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Abstract <p>This paper considers the classical Tricomi problem for the Lavrentiev–Bitsadze equation with a semi-strip in the elliptic part and a Frankl matching condition for the normal derivatives on the type-change line. Theorems on the uniqueness of the solution to the Tricomi problem, existence and uniqueness theorems for the solution to an auxiliary problem for the Laplace equation are proven, and integral representations for the first partial derivatives of the solution are obtained.</p>

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About the Tricomi Problem for the Lavrentiev–Bitsadze Equation with the Frankl Condition on the Type-change Line

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • N. Yu. Kapustin,
  • D. D. Vasilchenko

摘要

Abstract

This paper considers the classical Tricomi problem for the Lavrentiev–Bitsadze equation with a semi-strip in the elliptic part and a Frankl matching condition for the normal derivatives on the type-change line. Theorems on the uniqueness of the solution to the Tricomi problem, existence and uniqueness theorems for the solution to an auxiliary problem for the Laplace equation are proven, and integral representations for the first partial derivatives of the solution are obtained.