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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.12145 |
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| _version_ | 1866917593363775488 |
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| author | Colli, Pierluigi Kurima, Shunsuke Scarpa, Luca |
| author_facet | Colli, Pierluigi Kurima, Shunsuke Scarpa, Luca |
| contents | This paper deals with a nonlocal model for a hyperbolic phase field system coupling the standard energy balance equation for temperature with a dynamic for the phase variable: the latter includes an inertial term and a nonlocal convolution-type operator where the family of kernels depends on a small parameter. We rigorously study the asymptotic convergence of the system as the approximating parameter tends to zero and we obtain at the limit the local system with the elliptic laplacian operator acting on the phase variable. Our analysis is based on some asymptotic properties on nonlocal-to-local convergence that have been recently and successfully applied to families of Cahn--Hilliard models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12145 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlocal to local convergence of phase field systems with inertial term Colli, Pierluigi Kurima, Shunsuke Scarpa, Luca Analysis of PDEs This paper deals with a nonlocal model for a hyperbolic phase field system coupling the standard energy balance equation for temperature with a dynamic for the phase variable: the latter includes an inertial term and a nonlocal convolution-type operator where the family of kernels depends on a small parameter. We rigorously study the asymptotic convergence of the system as the approximating parameter tends to zero and we obtain at the limit the local system with the elliptic laplacian operator acting on the phase variable. Our analysis is based on some asymptotic properties on nonlocal-to-local convergence that have been recently and successfully applied to families of Cahn--Hilliard models. |
| title | Nonlocal to local convergence of phase field systems with inertial term |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.12145 |