| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2022-09-15T09:14:42Z |
| Last updated:
|
2024-11-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151026 |
| . |
| Reference:
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