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A new definition of Lie invariance for nonlinear multi-dimensional boundaryvalue problems (BVPs) is proposed by the generalization of known definitions tomuch wider classes of BVPs. The class of (1+3)-dimensional nonlinear BVPs ofthe Stefan type, modeling the process of melting and evaporation of metals, isstudied in detail. Using the definition proposed, the group classificationproblem for this class of BVPs is solved and some reductions (with physicalmeaning) to BVPs of lower dimensionality are made. Examples of how to constructexact solutions of the (1+3)-dimensional nonlinear BVP with thecorrectly-specified coefficients are presented.

Lie symmetries and reductions of multi-dimensional boundary value problems of the Stefan type