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 paramet...
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-02-01
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| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037424000931 |
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| Summary: | 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 Γ. |
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| ISSN: | 2590-0374 |