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.

中文翻译：

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确定具有特征类型变化线的混合抛物-双曲方程中的源函数

 抽象的

在本文中，我们研究了混合抛物线-双曲型模型方程的正问题和反问题。在直接问题中，考虑了该方程的 Tricomi 问题的模拟，具有类型变化的特征线。反问题的未知数是抛物线方程的 y 相关源函数。为了根据域抛物线部分中定义的解来确定它，指定了在点 \(x=x_{0}\) 处对于 \(y>0\) 条件的超定。证明了关于经典解意义上的问题的唯一可解性的局部定理。