Numerical study of a Transmission Problem in Elasticity with kind damping
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914411925471232 |
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| author | Ammari, Kais Komornik, Vilmos Sepúlveda, Mauricio Vera, Octavio |
| author_facet | Ammari, Kais Komornik, Vilmos Sepúlveda, Mauricio Vera, Octavio |
| contents | We investigate a transmission problem featuring a specific type of damping. Our primary focus is on analyzing the asymptotic behavior of the associated semigroup, $({\mathcal S}_{\mathcal A}(t))_{t\geq 0}$. We demonstrate that this semigroup exhibits a polynomial rate of decay towards zero when the initial data is taken over the domain ${\mathcal D}({\mathcal A})$. Furthermore, we establish that this decay rate is optimal. To support our theoretical findings, we present a comprehensive numerical study that validates and illustrates the sharpness of the obtained decay rates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_03043 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical study of a Transmission Problem in Elasticity with kind damping Ammari, Kais Komornik, Vilmos Sepúlveda, Mauricio Vera, Octavio Analysis of PDEs Optimization and Control 34B05, 34D05, 34H05 We investigate a transmission problem featuring a specific type of damping. Our primary focus is on analyzing the asymptotic behavior of the associated semigroup, $({\mathcal S}_{\mathcal A}(t))_{t\geq 0}$. We demonstrate that this semigroup exhibits a polynomial rate of decay towards zero when the initial data is taken over the domain ${\mathcal D}({\mathcal A})$. Furthermore, we establish that this decay rate is optimal. To support our theoretical findings, we present a comprehensive numerical study that validates and illustrates the sharpness of the obtained decay rates. |
| title | Numerical study of a Transmission Problem in Elasticity with kind damping |
| topic | Analysis of PDEs Optimization and Control 34B05, 34D05, 34H05 |
| url | https://arxiv.org/abs/2505.03043 |