Inverse Source Problem for the Subdiffusion Equation on a Metric Star Graph with Integral Overdetermination Condition

Abstract

In this article, it is investigated the inverse source problem for the subdiffusion equation on the metric star graph in Sobolev space with the integral overdetermination condition. The existence and uniqueness of the strong solution to the direct problem are proven with the functional method based on a priori estimates. The unique solvability of the inverse problem in the Sobolev space is proven. For that, we reduce the inverse source problem to the operator-based equation and prove that the corresponding resolvent operator is well-defined and continuous.

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DOI

10.1134/s1995080223120326

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