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 - <p style="text-align: justify;">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.</p>