
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
Abstract:
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.

