Year: 2018
Author: Dmitry Glotov, Willis E. Hames, A. J. Meir, Sedar Ngoma
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 4-5 : pp. 552–563
Abstract
We consider a problem of recovering the time-dependent diffusion coefficient in a parabolic system. To ensure uniqueness the system is constrained by the integral of the solution at all times. This problem has applications in geology where the parabolic equation models the accumulation and diffusion of argon in micas. Argon is generated by the decay of potassium and the diffusion is thermally activated. We introduce a time discretization, on which we base an application of Rothe’s method to prove existence of solutions. The numerical scheme corresponding to the semi-discretization exhibits convergence that is consistent with that in Euler’s method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-IJNAM-12530
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 4-5 : pp. 552–563
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Inverse problems integral constraint parabolic equation Rothe’s method geochronology.