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Radiogenic Source Identification for the Helium Production-Diffusion Equation

Published online by Cambridge University Press:  03 June 2015

Gang Bao ,
Todd A. Ehlers  and
Peijun Li
Gang Bao*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, China; Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Todd A. Ehlers*
Affiliation:
Department of Geosciences, Wilhelmstrasse 56, Universitä Tübingen, D-72074, Tübingen, Germany
Peijun Li*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
*
Email:todd.ehlers@uni-tuebingen.de
Corresponding author.Email:lipeijun@math.purdue.edu
Email:bao@math.msu.edu
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Abstract

Knowledge of helium diffusion kinetics is critical for materials in which helium measurements are made, particulary for thermochronology. In most cases the helium ages were younger than expected, an observation attributes to diffusive loss of helium and the ejection of high energy alpha particles. Therefore it is important to accurately calculate the distribution of the source term within a sample. In this paper, the prediction of the helium concentrations as function of a spatially variable source term are considered. Both the forward and inverse solutions are presented. Under the assumption of radially symmetric geometry, an analytical solution is deduced based on the eigenfunction expansion. Two regularization methods, the Tikhonov regularization and the spectral cutoff regularization, are considered to obtain the regularized solution. Error estimates with optimal convergence order are shown between the exact solution and the regularized solution. Numerical examples are presented to illustrate the validity and effectiveness of the proposed methods

Keywords

65M3235Q80Inverse source problemproduction-diffusion equationTikhonov regularization

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Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 1 , July 2013 , pp. 1 - 20
Copyright
Copyright © Global Science Press Limited 2013

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