边界上有集中势项的相场模型

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics Pub Date : 2025-02-01 DOI:10.1016/j.rinam.2024.100523

Ángela Jiménez-Casas

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引用次数: 0

摘要

本文分析了G. Caginalp（1986, 1991）和a . jimsamnez - casas - a的半线性相场模型的推广。Rodriguez-Bernal(1996, 2005)，其中我们考虑了一个集中在Γ邻域的奇异项，即域的边界。当一个参数趋于零时，邻域缩小到Γ。我们证明了新半线性相场模型的这组解，当该参数趋于零时，收敛于半线性相场问题的解，其中集中势转化为额外的通量条件在Γ上。

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Phase-field model with concentrating-potential terms on the boundary

In this paper we analyze a generalization of the semilinear phase field model from G. Caginalp (1986, 1991) and A. Jiménez-Casas-A. Rodriguez-Bernal (1996, 2005), where we consider a singular term concentrated in a neighborhood of

Γ

, the boundary of domain. The neighborhood shrinks to

Γ

as a parameter

ϵ

approaches zero.

We prove that this family of solutions, of the new semilinear phase field model, converges in suitable spaces when this parameter tends to zero, to the solutions of a semilinear phase field problem where the concentrating potential are transformed into an extra flux condition on