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Numerical Recovering of Space-Dependent Sources in Hyperbolic Transmission Problems

Author

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  • Miglena N. Koleva

    (Department of Mathematics, Faculty of Natural Sciences and Education, “Angel Kanchev” University of Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria)

  • Lubin G. Vulkov

    (Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, “Angel Kanchev” University of Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria)

Abstract

A body may have a structural, thermal, electromagnetic or optical role. In wave propagation, many models are described for transmission problems, whose solutions are defined in two or more domains. In this paper, we consider an inverse source hyperbolic problem on disconnected intervals, using solution point constraints. Applying a transform method, we reduce the inverse problems to direct ones, which are studied for well-posedness in special weighted Sobolev spaces. This means that the inverse problem is said to be well posed in the sense of Tikhonov (or conditionally well posed). The main aim of this study is to develop a finite difference method for solution of the transformed hyperbolic problems with a non-local differential operator and initial conditions. Numerical test examples are also analyzed.

Suggested Citation

  • Miglena N. Koleva & Lubin G. Vulkov, 2024. "Numerical Recovering of Space-Dependent Sources in Hyperbolic Transmission Problems," Mathematics, MDPI, vol. 12(11), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1748-:d:1408524
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    References listed on IDEAS

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    1. Martín-Vaquero, Jesús & Sajavičius, Svajūnas, 2019. "The two-level finite difference schemes for the heat equation with nonlocal initial condition," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 166-177.
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