Moving boundary identification for a two-dimensional inverse heat conduction problem.

In this article, we propose an algorithm for identifying a moving boundary in a 2D heat conduction equation without using initial data. The algorithm combines the method of lines and a quasi-reversibility method. The latter replaces the heat equation with a fourth-order partial differential equation, thereby stabilizing the problem. With the regularization parameters chosen suitably, the method can give an accurate approximation to the sought-for moving boundary. Numerical examples show that the proposed method is effective and stable. [ABSTRACT FROM AUTHOR]