Work

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

Year: 2024

Type: article

Abstract: In this paper we analyze a generalization of the semilinear phase field model from G. Caginalp (1986, 1991) and A. Jim\'enez-Casas-A. Rodriguez-Bernal (1996, 2005), when we consider a singular term concentrated in a neighborhood of the boundary of domain $\Gamma$. The neighborhood shrinks to $\Gamma$ as a parameter $\epsilon$ approaches zero. We prove that this family of solutions converges in suitable spaces when this parameter tends to zero, to the solutions of a semilinear phase field model where the concentrating potential are transformed into a flux condition on $\Gamma$.

Source: Results in Applied Mathematics

DOI: 10.1016/j.rinam.2024.100523

Author: Ángela Jiménez-Casas

Language: English

Topic: Solidification and crystal growth phenomena

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,490

Funder: Agencia Estatal de Investigación

Awards: G1790951275, G4085870282