Optimal Runge approximation for nonlocal wave equations and unique determination of polyhomogeneous nonlinearities
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916951242047488 |
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| author | Lin, Yi-Hsuan Tyni, Teemu Zimmermann, Philipp |
| author_facet | Lin, Yi-Hsuan Tyni, Teemu Zimmermann, Philipp |
| contents | The main purpose of this article is to establish the Runge-type approximation in $L^2(0,T;\widetilde{H}^s(Ω))$ for solutions of linear nonlocal wave equations. To achieve this, we extend the theory of very weak solutions for classical wave equations to our nonlocal framework. This strengthened Runge approximation property allows us to extend the existing uniqueness results for Calderón problems of linear and nonlinear nonlocal wave equations in our earlier works. Furthermore, we prove unique determination results for the Calderón problem of nonlocal wave equations with polyhomogeneous nonlinearities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13869 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Runge approximation for nonlocal wave equations and unique determination of polyhomogeneous nonlinearities Lin, Yi-Hsuan Tyni, Teemu Zimmermann, Philipp Analysis of PDEs Primary 35R30, Secondary 26A33, 42B37 The main purpose of this article is to establish the Runge-type approximation in $L^2(0,T;\widetilde{H}^s(Ω))$ for solutions of linear nonlocal wave equations. To achieve this, we extend the theory of very weak solutions for classical wave equations to our nonlocal framework. This strengthened Runge approximation property allows us to extend the existing uniqueness results for Calderón problems of linear and nonlinear nonlocal wave equations in our earlier works. Furthermore, we prove unique determination results for the Calderón problem of nonlocal wave equations with polyhomogeneous nonlinearities. |
| title | Optimal Runge approximation for nonlocal wave equations and unique determination of polyhomogeneous nonlinearities |
| topic | Analysis of PDEs Primary 35R30, Secondary 26A33, 42B37 |
| url | https://arxiv.org/abs/2408.13869 |