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Harmonic moments and an inverse problem for the heat equation
In the paper, we study an inverse problem for the heat equation. We introduce a class of bilinear forms on the space of harmonic polynomials ( called harmonic moments), which are represented by the Dirichlet-to-Neumann map. We investigate the uniqueness, stability, and reconstruction of the inverse...
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| Main Authors: | , , |
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| Format: | Default Preprint |
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1999
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| Online Access: | https://hdl.handle.net/2134/846 |
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| _version_ | 1818175104504299520 |
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| author | M. Kawashita Y.V. Kurylev H. Soga |
| author_facet | M. Kawashita Y.V. Kurylev H. Soga |
| author_sort | M. Kawashita (7160594) |
| collection | Figshare |
| description | In the paper, we study an inverse problem for the heat equation. We introduce a class of bilinear forms on the space of harmonic polynomials ( called harmonic moments), which are represented by the Dirichlet-to-Neumann map. We investigate the uniqueness, stability, and reconstruction of the inverse problem. The inverse data are given in the terms of the bilinear forms and can be exchanged into the data of the Dirichlet-to-Neumann map. The reconstruction ( of the density) is accomplished in two different ways: one is due to the idea of the mollifier and the other to the representation by the Carleman kernel in the complex analysis. The error terms are estimated depending on the degree of the harmonic polynomials. We estimates norms of the data on an arbitrary time interval by the norms on some fixed interval (e.g., 0 < t < 2). |
| format | Default Preprint |
| id | rr-article-9383684 |
| institution | Loughborough University |
| publishDate | 1999 |
| record_format | Figshare |
| spelling | rr-article-93836841999-01-01T00:00:00Z Harmonic moments and an inverse problem for the heat equation M. Kawashita (7160594) Y.V. Kurylev (7160063) H. Soga (7160597) Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified In the paper, we study an inverse problem for the heat equation. We introduce a class of bilinear forms on the space of harmonic polynomials ( called harmonic moments), which are represented by the Dirichlet-to-Neumann map. We investigate the uniqueness, stability, and reconstruction of the inverse problem. The inverse data are given in the terms of the bilinear forms and can be exchanged into the data of the Dirichlet-to-Neumann map. The reconstruction ( of the density) is accomplished in two different ways: one is due to the idea of the mollifier and the other to the representation by the Carleman kernel in the complex analysis. The error terms are estimated depending on the degree of the harmonic polynomials. We estimates norms of the data on an arbitrary time interval by the norms on some fixed interval (e.g., 0 < t < 2). 1999-01-01T00:00:00Z Text Preprint 2134/846 https://figshare.com/articles/preprint/Harmonic_moments_and_an_inverse_problem_for_the_heat_equation/9383684 CC BY-NC-ND 4.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified M. Kawashita Y.V. Kurylev H. Soga Harmonic moments and an inverse problem for the heat equation |
| title | Harmonic moments and an inverse problem for the heat equation |
| title_full | Harmonic moments and an inverse problem for the heat equation |
| title_fullStr | Harmonic moments and an inverse problem for the heat equation |
| title_full_unstemmed | Harmonic moments and an inverse problem for the heat equation |
| title_short | Harmonic moments and an inverse problem for the heat equation |
| title_sort | harmonic moments and an inverse problem for the heat equation |
| topic | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/846 |