Exact solutions of (1+1)-dimensional nonlinear boundary value problem with free boundaries

Abstract:
The (1+1)-dimensional nonlinear boundary value problem, modeling the process of melting and evaporation of metals, is studied by means of the classical Lie symmetry method. All possible Lie operators of the nonlinear heat equation, which allow to reduce the problem to boundary value problem for system of ordinary differential equations, are found. The forms of heat conductivity coefficients are established when the given problem can be analytically solved in explicit form.