Coefficient Inverse Problem for an Equation of Mixed Parabolic-Hyperbolic Type with a Noncharacteristic Line of Type Change

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-06-25 DOI:10.3103/s1066369x24700166

D. K. Durdiev

引用次数: 0

Abstract

In this paper, the direct and two inverse problems for a model equation of mixed parabolic-hyperbolic type are studied. In the direct problem, the Tricomi problem for this equation with a noncharacteristic line of type change is considered. The unknown of the inverse problem is the variable coefficient at the lowest derivative in the parabolic equation. To determine it, two inverse problems are studied: with respect to the solution defined in the parabolic part of the domain, the integral overdetermination condition (inverse problem 1) and one simple observation at a fixed point (inverse problem 2) are given. Theorems on the unique solvability of the formulated problems in the sense of a classical solution are proved.

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具有非特征类型变化线的抛物线-超抛物线混合型方程的系数反问题

摘要本文研究了抛物-双曲混合型模型方程的直接问题和两个逆问题。在直接问题中，考虑了该方程的 Tricomi 问题，该问题具有非特征线型变化。逆问题的未知数是抛物线方程最低导数处的可变系数。为了确定它，研究了两个逆问题：关于在域的抛物线部分定义的解，给出了积分超定条件（逆问题 1）和在定点的一个简单观测（逆问题 2）。在经典解的意义上，证明了所提问题的唯一可解性定理。

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

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.