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Volume 15, Issue 4-5
An Inverse Diffusion Coefficient Problem for a Parabolic Equation with Integral Constraint

Dmitry Glotov, Willis E. Hames, A. J. Meir & Sedar Ngoma

Int. J. Numer. Anal. Mod., 15 (2018), pp. 552-563.

Published online: 2018-04

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  • 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.

  • Keywords

Inverse problems, integral constraint, parabolic equation, Rothe’s method, geochronology.

  • AMS Subject Headings

35K20, 35R30, 86A22, 86A60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

dglotov@auburn.edu (Dmitry Glotov)

hameswe@auburn.edu (Willis E. Hames)

ajmeir@smu.edu (A. J. Meir)

nzb0015@auburn.edu (Sedar Ngoma)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-552, author = {Glotov , DmitryHames , Willis E.Meir , A. J. and Ngoma , Sedar}, title = {An Inverse Diffusion Coefficient Problem for a Parabolic Equation with Integral Constraint}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {4-5}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12530.html} }
TY - JOUR T1 - An Inverse Diffusion Coefficient Problem for a Parabolic Equation with Integral Constraint AU - Glotov , Dmitry AU - Hames , Willis E. AU - Meir , A. J. AU - Ngoma , Sedar JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 552 EP - 563 PY - 2018 DA - 2018/04 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12530.html KW - Inverse problems, integral constraint, parabolic equation, Rothe’s method, geochronology. AB -

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.

Dmitry Glotov, Willis E. Hames, A. J. Meir & Sedar Ngoma. (2020). An Inverse Diffusion Coefficient Problem for a Parabolic Equation with Integral Constraint. International Journal of Numerical Analysis and Modeling. 15 (4-5). 552-563. doi:
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