| Title:
|
On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients (English) |
| Author:
|
Harasim, Petr |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
56 |
| Issue:
|
5 |
| Year:
|
2011 |
| Pages:
|
459-480 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We apply a theoretical framework for solving a class of worst scenario problems to a problem with a nonlinear partial differential equation. In contrast to the one-dimensional problem investigated by P. Harasim in Appl. Math. 53 (2008), No. 6, 583–598, the two-dimensional problem requires stronger assumptions restricting the admissible set to ensure the monotonicity of the nonlinear operator in the examined state problem, and, as a result, to show the existence and uniqueness of the state solution. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. Furthermore, it is shown that the Galerkin approximation of the state solution can be calculated by means of the Kachanov method as the limit of a sequence of solutions to linearized problems. (English) |
| Keyword:
|
worst scenario problem |
| Keyword:
|
nonlinear differential equation |
| Keyword:
|
uncertain input parameters |
| Keyword:
|
Galerkin approximation |
| Keyword:
|
Kachanov method |
| MSC:
|
35D30 |
| MSC:
|
35G30 |
| MSC:
|
35J62 |
| MSC:
|
47H05 |
| MSC:
|
47J05 |
| MSC:
|
49M25 |
| MSC:
|
49N45 |
| MSC:
|
65J15 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 1249.35043 |
| idMR:
|
MR2852066 |
| DOI:
|
10.1007/s10492-011-0026-z |
| . |
| Date available:
|
2011-09-22T14:18:22Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141619 |
| . |
| 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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| Reference:
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| . |
