Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences


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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