Inverse source problem for the heat equation on a metric star graph with integral over-determination condition

Authors

Zarif Sobirov, National University of Uzbekistan, Tashkent, Uzbekistan; V.I.Romanovskiy Institute of Mathematics, Tashkent, UzbekistanFollow
Ariuxan Turemuratova, National University of Uzbekistan, Tashkent, Uzbekistan; Branch of Russian Economic University named after G.V.Plekhanov in Tashkent, Tashkent, UzbekistanFollow

Abstract

In this work we investigated an initial boundary value problem for the heat equation on a metric star graph in Sobolev space. The existence and uniqueness of the generalized solution are proved with the classical functional method based on a priori estimates. Also, we considered the inverse source problem with the integral over-determination condition. We reduced the inverse problem to the operator-based equation and proved that the corresponding resolvent operator is well-defined.

First Page

1

Last Page

15

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Recommended Citation

Sobirov, Zarif and Turemuratova, Ariuxan (2023) "Inverse source problem for the heat equation on a metric star graph with integral over-determination condition," Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 6: Iss. 1, Article 1.
DOI: https://doi.org/10.56017/2181-1318.1234