Inverse Problem of Finding the Time-dependent Coefficient of Heat Equation from Integral Overdetermination Condition Data

Abstract

In this paper we consider the problem of simultaneously determining the time-dependent thermal diffusivity and the temperature distribution in one-dimensional heat equation in the case of nonlocal boundary and integral overdetermination conditions. We establish conditions for the existence and uniqueness of a classical solution of the problem under considerations. We present some results on the numerical solution with an example.