| Title:
|
Determination of the unknown source term in a linear parabolic problem from the measured data at the final time (English) |
| Author:
|
Kaya, Müjdat |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
59 |
| Issue:
|
6 |
| Year:
|
2014 |
| Pages:
|
715-728 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The problem of determining the source term $F(x,t)$ in the linear parabolic equation $u_t=(k(x)u_x(x,t))_x + F(x,t)$ from the measured data at the final time $u(x,T)=\mu (x)$ is formulated. It is proved that the Fréchet derivative of the cost functional $J(F) = \|\mu _T(x)- u(x,T)\|_{0}^2$ can be formulated via the solution of the adjoint parabolic problem. Lipschitz continuity of the gradient is proved. An existence result for a quasi solution of the considered inverse problem is proved. A monotone iteration scheme is obtained based on the gradient method. Convergence rate is proved. (English) |
| Keyword:
|
inverse parabolic problem |
| Keyword:
|
unknown source |
| Keyword:
|
adjoint problem |
| Keyword:
|
Fréchet derivative |
| Keyword:
|
Lipschitz continuity |
| MSC:
|
35K10 |
| MSC:
|
35R30 |
| idZBL:
|
Zbl 06391458 |
| idMR:
|
MR3277735 |
| DOI:
|
10.1007/s10492-014-0081-3 |
| . |
| Date available:
|
2014-11-10T09:24:44Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143996 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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