Inverse source problem for the heat equation on a metric star graph with integral over-determination condition
Z. A. SobirovNational University of Uzbekistan, Tashkent, Uzbekistan;
V.I.Romanovskiy Institute of Mathematics, Tashkent, UzbekistanA. A. TuremuratovaNational University of Uzbekistan, Tashkent, Uzbekistan; Branch of Russian Economic University named after G.V.Plekhanov in Tashkent, Tashkent, Uzbekistan
2023en
Ochiq kirishBronza
ABI
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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.
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