Determining a Source Function in the Mixed Parabolic–Hyperbolic Equation with Characteristic Type Change Line

IF 0.8 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI:10.1134/s1995080224600584

D. K. Durdiev, D. A. Toshev, H. H. Turdiev

引用次数: 0

Abstract

In this paper, we study the direct and inverse problems for a model equation of a mixed parabolic-hyperbolic type. In the direct problem, an analog of the Tricomi problem for this equation with a characteristic line of type change is considered. The unknown of the inverse problem is the y-dependent source function of the parabolic equation. To determine it with respect to the solution defined in the parabolic part of the domain, an overdetermination at the point \(x=x_{0}\) for \(y>0\) condition is specified. Local theorems on the unique solvability of the problems posed in the sense of the classical solution are proved.

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确定具有特征类型变化线的抛物线-双曲混合方程中的源函数

摘要本文研究了抛物-双曲混合型模型方程的直接问题和逆问题。在直接问题中，我们考虑了该方程的 Tricomi 问题的类似问题，其特征线类型发生了变化。逆问题的未知数是抛物线方程的 y 依赖源函数。为了确定它与定义在抛物线部分域中的解的关系，在点\(x=x_{0}\)处指定了一个\(y>0\)条件的过度确定。证明了在经典解的意义上所提出问题的唯一可解性的局部定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Lobachevskii Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

42.90%

发文量

127

期刊介绍： Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.