TY - EJOU
AU - Huntul, M. J.
AU - Lesnic, D.
TI - Determination of Time-Dependent Coefficients for a Weakly Degenerate Heat Equation
T2 - Computer Modeling in Engineering \& Sciences
PY - 2020
VL - 123
IS - 2
SN - 1526-1506
AB - 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 *lsqnonlin*. For both exact
and noisy input data, accurate and stable numerical results are obtained.
KW - Inverse problem
KW - weakly degenerate heat equation
KW - Tikhonovâ€™s regularization
DO - 10.32604/cmes.2020.08791