Article
| Title: | Application of Rothe's method to a parabolic inverse problem with nonlocal boundary condition (English) |
| Author: | Jo, Yong-Hyok |
| Author: | Ri, Myong-Hwan |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 67 |
| Issue: | 5 |
| Year: | 2022 |
| Pages: | 573-592 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We consider an inverse problem for the determination of a purely time-dependent source in a semilinear parabolic equation with a nonlocal boundary condition. An approximation scheme for the solution together with the well-posedness of the problem with the initial value $u_0\in H^1(\Omega )$ is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe's method is constructed for the problem when $u_0\in L^2(\Omega )$ and the integral kernel in the nonlocal boundary condition is symmetric. (English) |
| Keyword: | Rothe's method |
| Keyword: | nonlocal boundary condition |
| Keyword: | semilinear parabolic equation |
| Keyword: | inverse source problem |
| MSC: | 35K58 |
| MSC: | 35R30 |
| MSC: | 65M20 |
| idZBL: | Zbl 07613013 |
| idMR: | MR4484887 |
| DOI: | 10.21136/AM.2021.0029-21 |
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| Date available: | 2022-09-15T09:14:42Z |
| Last updated: | 2022-12-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151026 |
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