Solving the backward heat equation on the unit sphere

Quoc Thong Le Gia; Huy Tuan Nguyen; Thanh Tran

doi:10.21914/anziamj.v56i0.9346

Authors

Quoc Thong Le Gia School of Mathematics and Statistics, University of New South Wales, Sydney, Australia.
Huy Tuan Nguyen Department of Mathematics and Informatics, HCMC University of Science, Vietnam National University, Viet Nam
Thanh Tran School of Mathematics and Statistics, University of New South Wales, Sydney, Australia.

DOI:

https://doi.org/10.21914/anziamj.v56i0.9346

Keywords:

backward heat equation, unit sphere, radial basis function

Abstract

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. References

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Author Biography

Quoc Thong Le Gia, School of Mathematics and Statistics, University of New South Wales, Sydney, Australia.

I am a Lecturer in Applied Mathemetics at the University of New South Wales, Sydney, Australia.