A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910708930707456 |
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| author | Claes, Leander Lankeit, Johannes Winkler, Michael |
| author_facet | Claes, Leander Lankeit, Johannes Winkler, Michael |
| contents | A model for the generation of heat due to mechanical losses during acoustic wave propagation in a solid is considered in a Kelvin-Voigt type framework. In contrast to previous studies on related thermoviscoelastic models, in line with recent experimental findings the present manuscript focuses on situations in which elastic parameters depend on temperature. Despite an apparent loss of mathematically favorable structural properties thereby encountered, in the framework of a suitably generalized concept of solvability a result on global existence of solutions is derived under mild assumptions which, in particular, do not involve any smallness condition on the initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions Claes, Leander Lankeit, Johannes Winkler, Michael Analysis of PDEs 35D99 (primary), 35L05, 74F05, 74J10 (secondary) A model for the generation of heat due to mechanical losses during acoustic wave propagation in a solid is considered in a Kelvin-Voigt type framework. In contrast to previous studies on related thermoviscoelastic models, in line with recent experimental findings the present manuscript focuses on situations in which elastic parameters depend on temperature. Despite an apparent loss of mathematically favorable structural properties thereby encountered, in the framework of a suitably generalized concept of solvability a result on global existence of solutions is derived under mild assumptions which, in particular, do not involve any smallness condition on the initial data. |
| title | A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions |
| topic | Analysis of PDEs 35D99 (primary), 35L05, 74F05, 74J10 (secondary) |
| url | https://arxiv.org/abs/2411.14900 |