An inverse non-Fourier heat conduction problem approach for estimating the boundary condition in electronic device (Q1776674)

The two-dimensional time-dependent hyperbolic heat conduction equation is investigated. The initial conditions and the Dirichlet conditions on three sides of the square domain are homogeneous. The temperature on the fourth side is determined from interior temperature measurements which may also contain some errors. No regularization is required, just an ordinary linear least-squares inversion, and it is not clear if the problem is ill-posed. It might be interesting to use the boundary element method instead of the finite difference method for the direct solver.