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A class of moving boundary problems with a source term: application of a reciprocal transformation

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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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Funding

Partial financial support was received from European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 823731 CONMECH and the Project 80020210100002“Soluciones exactas en problemas de frontera libre”from Austral University, Rosario, Argentina and CONICET.

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Authors and Affiliations

  1. Departamento. de Matemática, FCE Universidad Austral, Paraguay, 1950, Rosario, Argentina

    Adriana C. Briozzo & Domingo A. Tarzia

  2. CONICET, Rosario, Argentina

    Adriana C. Briozzo & Domingo A. Tarzia

  3. School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia

    Colin Rogers

Authors
  1. Adriana C. Briozzo
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  2. Colin Rogers
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  3. Domingo A. Tarzia
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Contributions

All authors contributed to the study conception and design. The first draft of the manuscript was written by C.Rogers and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Adriana C. Briozzo.

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Briozzo, A.C., Rogers, C. & Tarzia, D.A. A class of moving boundary problems with a source term: application of a reciprocal transformation. Acta Mech 234, 1889–1900 (2023). https://doi.org/10.1007/s00707-023-03477-7

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  • DOI: https://doi.org/10.1007/s00707-023-03477-7

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