Control of waves on Lorentzian manifolds with curvature bounds
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914952084717568 |
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| author | Jena, Vaibhav Kumar Shao, Arick |
| author_facet | Jena, Vaibhav Kumar Shao, Arick |
| contents | We prove boundary controllability results for wave equations (with lower-order terms) on Lorentzian manifolds with time-dependent geometry satisfying suitable curvature bounds. The main ingredient is a novel global Carleman estimate on Lorentzian manifolds that is supported in the exterior of a null (or characteristic) cone, which leads to both an observability inequality and bounds for the corresponding constant. The Carleman estimate also yields a unique continuation result on the null cone exterior, which has applications toward inverse problems for linear waves on Lorentzian backgrounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_09539 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Control of waves on Lorentzian manifolds with curvature bounds Jena, Vaibhav Kumar Shao, Arick Analysis of PDEs We prove boundary controllability results for wave equations (with lower-order terms) on Lorentzian manifolds with time-dependent geometry satisfying suitable curvature bounds. The main ingredient is a novel global Carleman estimate on Lorentzian manifolds that is supported in the exterior of a null (or characteristic) cone, which leads to both an observability inequality and bounds for the corresponding constant. The Carleman estimate also yields a unique continuation result on the null cone exterior, which has applications toward inverse problems for linear waves on Lorentzian backgrounds. |
| title | Control of waves on Lorentzian manifolds with curvature bounds |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2112.09539 |