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

2022/07/18 by Adriana C. Briozzo, C. Rogers, Briozzo, Adriana C. +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2207.08907

openalex publication_date 2022/07/18 · openalex created_date 2022/07/21 · openalex updated_date 2026/07/28

Abstract

We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a class of boundary value problems for the nonlinear canonical evolution equation involving a source term with two free boundaries. This equivalence is obtained by applying a reduction to a Burgers equation and a reciprocal-type transformations. Moreover, for a particular case, we obtain a unique explicit solution for the two different problems.

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