Solving the backward heat equation on the unit sphere

Quoc Thong Le Gia, Huy Tuan Nguyen, Thanh Tran


We consider an inverse problem for the heat equation on the unit sphere in which the final (current) temperature on the sphere is given, and the task is to determine the initial temperature. The problem is ill-posed in the sense of Hadamard; hence, a regularization technique is applied. We then use a Galerkin method with spherical radial basis functions to solve the regularized problem. The problem may have potential applications in atmospheric modelling, when current temperature data is used to calculate a past global temperature.



backward heat equation, unit sphere, radial basis function

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.