학술논문
A class of moving boundary problems with a source term: application of a reciprocal transformation.
Document Type
Article
Source
Subject
*NONLINEAR boundary value problems
*BOUNDARY value problems
*BURGERS' equation
*NONLINEAR evolution equations
*HEAT equation
*PHASE transitions
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Language
ISSN
0001-5970
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. [ABSTRACT FROM AUTHOR]