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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.12448 |
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| _version_ | 1866910877704257536 |
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| author | Lassas, Matti |
| author_facet | Lassas, Matti |
| contents | We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is based on self-interaction of linearized waves or other solutions in the presence of non-linearities. Multiple linearization has successfully been used to solve inverse problems for non-linear equation which are still unsolved for the corresponding linear equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12448 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Introduction to inverse problems for non-linear partial differential equations Lassas, Matti Analysis of PDEs 35R30: Inverse problems (undetermined coefficients, etc.) for PDE We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is based on self-interaction of linearized waves or other solutions in the presence of non-linearities. Multiple linearization has successfully been used to solve inverse problems for non-linear equation which are still unsolved for the corresponding linear equations. |
| title | Introduction to inverse problems for non-linear partial differential equations |
| topic | Analysis of PDEs 35R30: Inverse problems (undetermined coefficients, etc.) for PDE |
| url | https://arxiv.org/abs/2503.12448 |