@Article{cmes.2020.08791,
AUTHOR = {M. J. Huntul, D. Lesnic},
TITLE = {Determination of Time-Dependent Coefficients for a Weakly Degenerate Heat Equation},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {123},
YEAR = {2020},
NUMBER = {2},
PAGES = {475--494},
URL = {http://www.techscience.com/CMES/v123n2/38687},
ISSN = {1526-1506},
ABSTRACT = {In this paper, we consider solving numerically for the first time inverse problems
of determining the time-dependent thermal diffusivity coefficient for a weakly degenerate
heat equation, which vanishes at the initial moment of time, and/or the convection
coefficient along with the temperature for a one-dimensional parabolic equation, from
some additional information about the process (the so-called over-determination
conditions). Although uniquely solvable these inverse problems are still ill-posed since
small changes in the input data can result in enormous changes in the output solution.
The finite difference method with the Crank-Nicolson scheme combined with the
nonlinear Tikhonov regularization are employed. The resulting minimization problem is
computationally solved using the MATLAB toolbox routine <i>lsqnonlin</i>. For both exact
and noisy input data, accurate and stable numerical results are obtained.},
DOI = {10.32604/cmes.2020.08791}
}