Determination of a time-dependent heat transfer coefficient in a nonlinear inverse heat conduction problem

In this article, the determination of the time-dependent heat transfer coefficient, involving nonlinear boundary conditions of the third kind in the one-dimensional transient heat conduction from a non-standard boundary measurement is investigated. For this inverse, nonlinear, ill-posed problem, the existence and uniqueness of the solution are proved. Numerical results are obtained, using the boundary element method, and discussed.