Symmetry in Nonlinear Mathematical Physics - 2009

Roman Cherniha (Institute of Mathematics, Kyiv, Ukraine & Lesya Ukrainka Volyn National University, Lutsk, Ukraine)

Lie symmetries and nonlinear boundary value problems of Stefan type

A class of nonlinear boundary value problems with moving boundaries, which arise in modeling the process of melting and evaporation of metals, is studied. The reduction of such problems by means of Lie symmetries to those of lower dimensionality is presented. All possible Lie operators of the nonlinear heat equation, which allow to reduce the (1+1)-dimensional problem to boundary value problem for system of ODEs, are found. Examples of the reduction of (1+3)-dimensional problem to those of lower dimensionality are also presented and the corresponding solutions constructed.