Direct and inverse problems for the heat equation with a dynamic-type boundary condition

Abstract

This paper considers the initial-boundary value problem for the heat equation with a dynamic-type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon the data of the classical solution are shown by using the generalized Fourier method. This paper also investigates the inverse problem of finding a time-dependent coefficient of the heat equation from the data of integral overdetermination condition.