Well-posedness of a Pseudo-Parabolic KWC System in Materials Science
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929245605855232 |
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| author | Antil, Harbir Mizuno, Daiki Shirakawa, Ken |
| author_facet | Antil, Harbir Mizuno, Daiki Shirakawa, Ken |
| contents | The original KWC-system is widely used in materials science. It was proposed in [Kobayashi et al, Physica D, 140, 141--150 (2000)] and is based on the phase field model of planar grain boundary motion. This model suffers from two key challenges. Firstly, it is difficult to establish its relation to physics, in particular, a variational model. Secondly, it lacks uniqueness. The former has been recently studied within the realm of BV-theory. The latter only holds under various simplifications. This article introduces a pseudo-parabolic version of the KWC-system. A direct relationship with variational model (as gradient-flow) and uniqueness are established without making any unrealistic simplifications. Namely, this is the first KWC-system which is both physically and mathematically valid. The proposed model overcomes the well-known open issues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10413 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness of a Pseudo-Parabolic KWC System in Materials Science Antil, Harbir Mizuno, Daiki Shirakawa, Ken Analysis of PDEs 35A15, 35G50, 35G61, 35K70, 74N20 The original KWC-system is widely used in materials science. It was proposed in [Kobayashi et al, Physica D, 140, 141--150 (2000)] and is based on the phase field model of planar grain boundary motion. This model suffers from two key challenges. Firstly, it is difficult to establish its relation to physics, in particular, a variational model. Secondly, it lacks uniqueness. The former has been recently studied within the realm of BV-theory. The latter only holds under various simplifications. This article introduces a pseudo-parabolic version of the KWC-system. A direct relationship with variational model (as gradient-flow) and uniqueness are established without making any unrealistic simplifications. Namely, this is the first KWC-system which is both physically and mathematically valid. The proposed model overcomes the well-known open issues. |
| title | Well-posedness of a Pseudo-Parabolic KWC System in Materials Science |
| topic | Analysis of PDEs 35A15, 35G50, 35G61, 35K70, 74N20 |
| url | https://arxiv.org/abs/2402.10413 |