论文标题
带有源术语的一类移动边界问题。互惠转换的应用
A Class of Moving Boundary Problems with a Source Term. Application of a Reciprocal Transformation
论文作者
论文摘要
我们考虑了一个新的Stefan型问题，用于经典的热量方程，并根据可变时间的潜热和相变温度。我们证明了这个Stefan问题的等效性与非线性规范进化方程的一类边界价值问题，该方程涉及具有两个自由边界的源项。通过将还原应用于汉堡方程和相互型转换来获得这种等效性。此外，对于特定情况，我们为两个不同问题获得了独特的明确解决方案。
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.
