Inverse Problem for Mixed-type Equation with an Elliptic Operator of Arbitrary Order

Inverse Problem for Mixed-type Equation with an Elliptic Operator of Arbitrary Order

In this paper, we consider the inverse problem of determining the source function for a mixed-type equation with a positive elliptic operator. The existence and uniqueness of the solution of the posed inverse problem are proved. And also a generalized solution of the problem is introduced and the st...

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Veröffentlicht in:Lobachevskii journal of mathematics 2023-02, Vol.44 (2), p.533-541
Hauptverfasser: Ashurov, R. R., Murzambetova, M. B.
Format: Artikel
Sprache:eng
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Algebra
Analysis
Forward problem
Geometry
Inverse problems
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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Murzambetova, M. B.
description In this paper, we consider the inverse problem of determining the source function for a mixed-type equation with a positive elliptic operator. The existence and uniqueness of the solution of the posed inverse problem are proved. And also a generalized solution of the problem is introduced and the stability of such a solution is proved. At the end of the paper, a mixed-type equation with a non-negative elliptic operator is considered. It is proved that the corresponding inverse problem also has a unique solution, although, as is known, the forward problem for such an equation has more than one solution.
doi_str_mv 10.1134/S1995080223020105
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subjects Algebra
Analysis
Forward problem
Geometry
Inverse problems
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
title Inverse Problem for Mixed-type Equation with an Elliptic Operator of Arbitrary Order
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