Inverse coefficient problems for mathematical models of one-dimensional heat transfer with a generalized condition of preservation of medium temperature

摘要

In this short note we study an inverse problem for the heat equation which is motivated by some mathematical models describing the process of heat transfer in a homogeneous bar with the prescribed law of changes of the average temperature. It is proved that the considered inverse problem has a unique generalized solution.The main difficulty of solving this type of problems is that the system of eigenfunctions of the multiple differentiation operator subject to boundary conditions of the initial problem does not have the basis property.