On determining and breaking the gauge class in inverse problems for reaction-diffusion equations
We investigate an inverse boundary value problem of determination of a nonlinear law for reaction-diffusion processes, which are modeled by general form semilinear parabolic equations. We do not assume that any solutions to these equations are known a priori, in which case the problem has a well-kno...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2024-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424000185/type/journal_article |
| _version_ | 1827341439678283776 |
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| author | Yavar Kian Tony Liimatainen Yi-Hsuan Lin |
| author_facet | Yavar Kian Tony Liimatainen Yi-Hsuan Lin |
| author_sort | Yavar Kian |
| collection | DOAJ |
| description | We investigate an inverse boundary value problem of determination of a nonlinear law for reaction-diffusion processes, which are modeled by general form semilinear parabolic equations. We do not assume that any solutions to these equations are known a priori, in which case the problem has a well-known gauge symmetry. We determine, under additional assumptions, the semilinear term up to this symmetry in a time-dependent anisotropic case modeled on Riemannian manifolds, and for partial data measurements on
${\mathbb R}^n$
. |
| first_indexed | 2024-03-07T21:41:07Z |
| format | Article |
| id | doaj.art-fc3e83e8c3394567a860cca88aa515bf |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-03-07T21:41:07Z |
| publishDate | 2024-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-fc3e83e8c3394567a860cca88aa515bf2024-02-26T09:29:34ZengCambridge University PressForum of Mathematics, Sigma2050-50942024-01-011210.1017/fms.2024.18On determining and breaking the gauge class in inverse problems for reaction-diffusion equationsYavar Kian0https://orcid.org/0000-0002-5588-3600Tony Liimatainen1Yi-Hsuan Lin2https://orcid.org/0000-0002-5667-9249Univ Rouen Normandie, CNRS, Normandie Univ, LMRS UMR 6085, F-76000 Rouen, France; E-mail:Department of Mathematics and Statistics, University of Helsinki, P.O 68 (Pietari Kalmin katu 5), Helsinki, Finland; E-mail:Department of Applied Mathematics, National Yang Ming Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu, 30050, Taiwan; E-mail:We investigate an inverse boundary value problem of determination of a nonlinear law for reaction-diffusion processes, which are modeled by general form semilinear parabolic equations. We do not assume that any solutions to these equations are known a priori, in which case the problem has a well-known gauge symmetry. We determine, under additional assumptions, the semilinear term up to this symmetry in a time-dependent anisotropic case modeled on Riemannian manifolds, and for partial data measurements on ${\mathbb R}^n$ .https://www.cambridge.org/core/product/identifier/S2050509424000185/type/journal_article35R3035K1035K55 |
| spellingShingle | Yavar Kian Tony Liimatainen Yi-Hsuan Lin On determining and breaking the gauge class in inverse problems for reaction-diffusion equations Forum of Mathematics, Sigma 35R30 35K10 35K55 |
| title | On determining and breaking the gauge class in inverse problems for reaction-diffusion equations |
| title_full | On determining and breaking the gauge class in inverse problems for reaction-diffusion equations |
| title_fullStr | On determining and breaking the gauge class in inverse problems for reaction-diffusion equations |
| title_full_unstemmed | On determining and breaking the gauge class in inverse problems for reaction-diffusion equations |
| title_short | On determining and breaking the gauge class in inverse problems for reaction-diffusion equations |
| title_sort | on determining and breaking the gauge class in inverse problems for reaction diffusion equations |
| topic | 35R30 35K10 35K55 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424000185/type/journal_article |
| work_keys_str_mv | AT yavarkian ondeterminingandbreakingthegaugeclassininverseproblemsforreactiondiffusionequations AT tonyliimatainen ondeterminingandbreakingthegaugeclassininverseproblemsforreactiondiffusionequations AT yihsuanlin ondeterminingandbreakingthegaugeclassininverseproblemsforreactiondiffusionequations |