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

被引：1
|
作者：
Briozzo, Adriana C. [1 ,2 ]
Rogers, Colin [3 ]
Tarzia, Domingo A. [1 ,2 ]
机构：
[1] FCE Univ Austral, Dept Matemat, RA-1950 Rosario, Argentina
[2] Consejo Nacl Invest Cient & Tecn, Rosario, Argentina
[3] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia
来源：
ACTA MECHANICA | 2023年 / 234卷 / 05期
关键词：
STEFAN PROBLEM; LATENT-HEAT; BACKLUND; CONJUGATION; HETEROGENEITY; INFILTRATION; EQUATION;
D O I：
10.1007/s00707-023-03477-7
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
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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页码：1889 / 1900
页数：12
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