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This paper considers the initial-boundary value problem for the heat equationwith a dynamic type boundary condition. Under some regularity, consistency andorthogonality conditions, the existence, uniqueness and continuous dependenceupon the data of the classical solution are shown by using the generalizedFourier method. This paper also investigates the inverse problem of finding atime-dependent coefficient of the heat equation from the data of integraloverdetermination condition.

Direct and Inverse Problems for the Heat Equation with a Dynamic type Boundary Condition