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Unique Continuation Property with Partial Information for Two-Dimensional Anisotropic Elasticity Systems
| Title: | Unique Continuation Property with Partial Information for Two-Dimensional Anisotropic Elasticity Systems |
| Authors: | Cheng, Jin Browse this author | | Liu, Yi-kan Browse this author | | Wang, Yan-bo Browse this author | | Yamamoto, Masahiro Browse this author |
| Keywords: | anisotropic elasticity system | | unique continuation | | Riemann function |
| Issue Date: | Jan-2020 |
| Publisher: | Springer |
| Journal Title: | Acta mathematicae applicatae sinica-english series |
| Volume: | 36 |
| Issue: | 1 |
| Start Page: | 3 |
| End Page: | 17 |
| Publisher DOI: | 10.1007/s10255-020-0910-y |
| Abstract: | In this paper, we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information. More precisely, given a homogeneous elasticity system in a connected open bounded domain, we investigate the unique continuation by assuming only the vanishing of one component of the solution in a subdomain. Using the corresponding Riemann function, we prove that the solution vanishes in the whole domain provided that the other component vanishes at one point up to its second derivatives. Further, we construct several examples showing the possibility of further reducing the additional information of the other component. This result possesses remarkable significance in both theoretical and practical aspects because the required data are almost halved for the unique determination of the whole solution. |
| Publisher URI: | https://arxiv.org/abs/1903.11930 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/76703 |
| Appears in Collections: | 電子科学研究所 (Research Institute for Electronic Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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