An Inverse Diffusion Coefficient Problem for a Parabolic Equation with Integral Constraint

An Inverse Diffusion Coefficient Problem for a Parabolic Equation with Integral Constraint

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.

Author Details

Dmitry Glotov

Willis E. Hames

A. J. Meir

Sedar Ngoma