Symmetry analysis and exact solutions of one class of (1+3)-dimensional boundary-value problems of the Stefan type

TL;DR

This paper performs symmetry analysis and constructs exact solutions for a class of complex (1+3)-dimensional Stefan boundary-value problems modeling metal melting and evaporation.

Contribution

It provides a comprehensive group classification and derives exact solutions for a specific class of nonlinear boundary-value problems of the Stefan type.

Findings

Group classification of the boundary-value problems achieved.

Exact solutions constructed for a particular problem within the class.

Results facilitate understanding of melting and evaporation processes in metals.

Abstract

We present the group classification of one class of (1+3)-dimensional nonlinear boundary-value problems of the Stefan type that simulate the processes of melting and evaporation of metals. The results obtained are used for the construction of the exact solution of one boundary-value problem from the class under study.