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The problem of recovering a time-dependent coefficient in a parabolic partial differential equation has attracted considerable attention in the classical literature on inverse heat conduction problems. In this article, the Ritz–Galerkin method with satisfier function is utilized to solve the inverse problems of identifying the temperature    and the unknown diffusion coefficient    in the one-dimensional heat equation from various additional information. Numerical examples are presented and discussed.

Satisfier function in Ritz–Galerkin method for the identification of a time-dependent diffusivity