Abstract
This paper investigates the reconstruction of time-dependent coefficients in the transient heat equation in a moving boundary domain with unknown free boundaries. This problem is considered under Stefan/heat moments overdetermination conditions also dependent of time. This inverse problem is nonlinear. Moreover, although local existence and uniqueness of solution hold, the problem is still ill-posed since small errors into the input data lead to large errors in the reconstructed coefficients. In order to obtain a stable solution, the nonlinear Tikhonov regularization method is employed. This recasts as minimizing a regularization functional subject to simple bounds on variables. Numerically, this is accomplished using the Matlab toolbox optimization routine lsqnonlin. Numerical results illustrate that stable and accurate solutions are obtained.
Disclosure statement
No potential conflict of interest was reported by the authors.