Lie symmetry of a class of nonlinear boundary value problems with free boundaries

TL;DR

This paper applies Lie symmetry methods to a class of nonlinear boundary value problems modeling melting and evaporation, introducing a new invariance definition for BVPs.

Contribution

It develops a novel definition of invariance in Lie's sense specifically for boundary value problems and applies it to a class modeling phase change processes.

Findings

New invariance definition for BVPs introduced

Lie symmetry analysis performed on melting and evaporation models

Potential for symmetry-based solution methods for phase change problems

Abstract

A class of (1+1)--dimensional nonlinear boundary value problems (BVPs), modeling the process of melting and evaporation of solid materials, is studied by means of the classical Lie symmetry method. New definition of invariance in Lie's sense for BVP is presented and applied for the class of BVPs in question.