TY - JOUR
T1 - Free Boundary Determination in Nonlinear Diffusion
AU - M. S. Hussein, D. Lesnic & M. Ivanchov
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 295
EP - 310
PY - 2018
DA - 2018/02
SN - 3
DO - http://doi.org/10.4208/eajam.100913.061113a
UR - https://global-sci.org/intro/article_detail/eajam/10859.html
KW - Nonlinear diffusion, free boundary problem, finite difference method.
AB - <p style="text-align: justify;">Free boundary problems with nonlinear diffusion occur in various applications,
such as solidification over a mould with dissimilar nonlinear thermal properties
and saturated or unsaturated absorption in the soil beneath a pond. In this article,
we consider a novel inverse problem where a free boundary is determined from the
mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem,
and a stability estimate is established. The problem is recast as a nonlinear least-squares
minimisation problem, which is solved numerically using the lsqnonlin routine
from the MATLAB toolbox. Accurate and stable numerical solutions are achieved. For
noisy data, instability is manifest in the derivative of the moving free surface, but not in
the free surface itself nor in the concentration or temperature.</p>