Optimization Related to Some Nonlocal Problems of Kirchhoff Type
| Autor: | Mohsen Zivari-Rezapour, Behrouz Emamizadeh, Amin Farjudian |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Characteristic function (convex analysis)
0209 industrial biotechnology Optimization problem General Mathematics Admissible set 02 engineering and technology Maximization Type (model theory) Convexity 020901 industrial engineering & automation 0202 electrical engineering electronic engineering information engineering Free boundary problem Applied mathematics 020201 artificial intelligence & image processing Mathematics Energy functional |
| Zdroj: | Canadian Journal of Mathematics. 68:521-540 |
| ISSN: | 1496-4279 0008-414X |
| DOI: | 10.4153/cjm-2015-040-9 |
| Popis: | In this paper we introduce two rearrangement optimization problems, one being a maximization and the other a minimization problem, related to a nonlocal boundary value problem of Kirchhoff type. Using the theory of rearrangements as developed by G. R. Burton, we are able to show that both problems are solvable and derive the corresponding optimality conditions. These conditions in turn provide information concerning the locations of the optimal solutions.The strict convexity of the energy functional plays a crucial role in both problems. The popular case in which the rearrangement class (i.e., the admissible set) is generated by a characteristic function is also considered. We show that in this case, the maximization problem gives rise to a free boundary problem of obstacle type, which turns out to be unstable. On the other hand, the minimization problem leads to another free boundary problem of obstacle type that is stable. Some numerical results are included to conûrm the theory. |
| Databáze: | OpenAIRE |
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