Determination of time-dependent coefficients in moving boundary problems under nonlocal and heat moment observations

• Published in: International journal of computational methods in engineering science and mechanics Vol. 22; no. 6; pp. 500 - 513
• Main Authors: Adil, Z., Hussein, M. S., Lesnic, D.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 02.11.2021
• Subjects: coefficient identification problem; equation; inverse problem; Moving boundary problem; nonlinear optimization; reaction-diffusion
• ISSN: 1550-2287; 1550-2295
• DOI: 10.1080/15502287.2021.1892870

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.