Determination of unknown thermal coefficients in a non-classical Stefan problem

Abstract

We study a non-classical one phase Stefan problem with a particular control function which depends on the evolution of the temperature at the fixed face x=0 and, we assume a Neumann boundary condition and an over specified Robin condition at the fixed face. Under certain restrictions on the data an explicit similarity type solution is given. Moreover, we determine the free boundary and one unknown thermal coefficient, or two unknown thermal coefficients depending on whether the direct or inverse Stefan problem is considered.