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We consider a new Stefan-type problem for the classical heat equation with alatent heat and phase-change temperature depending of the variable time. Weprove the equivalence of this Stefan problem with a class of boundary valueproblems for the nonlinear canonical evolution equation involving a source termwith two free boundaries. This equivalence is obtained by applying a reductionto a Burgers equation and a reciprocal-type transformations. Moreover, for aparticular case, we obtain a unique explicit solution for the two differentproblems.

A Class of Moving Boundary Problems with a Source Term. Application of a Reciprocal Transformation