Fréchet Differentiability for a Damped Kirchhoff-Type Equation and Its Application to Bilinear Minimax Optimal Control Problems
We consider a damped Kirchhoff-type equation with Dirichlet boundary conditions. The objective is to show the Fréchet differentiability of a nonlinear solution map from a bilinear control input to the solution of a Kirchhoff-type equation. We use this result to formulate the minimax optimal control...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2019/3238462 |
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| _version_ | 1849400794870185984 |
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| author | Jin-soo Hwang |
| author_facet | Jin-soo Hwang |
| author_sort | Jin-soo Hwang |
| collection | DOAJ |
| description | We consider a damped Kirchhoff-type equation with Dirichlet boundary conditions. The objective is to show the Fréchet differentiability of a nonlinear solution map from a bilinear control input to the solution of a Kirchhoff-type equation. We use this result to formulate the minimax optimal control problem. We show the existence of optimal pairs and find their necessary optimality conditions. |
| format | Article |
| id | doaj-art-8daa18c966a54bedb2e2c4bc8ec7e8c9 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-8daa18c966a54bedb2e2c4bc8ec7e8c92025-08-20T03:37:54ZengWileyInternational Journal of Differential Equations1687-96431687-96512019-01-01201910.1155/2019/32384623238462Fréchet Differentiability for a Damped Kirchhoff-Type Equation and Its Application to Bilinear Minimax Optimal Control ProblemsJin-soo Hwang0Department of Mathematics Education, College of Education, Daegu University, Jillyang, Gyeongsan, Gyeongbuk, Republic of KoreaWe consider a damped Kirchhoff-type equation with Dirichlet boundary conditions. The objective is to show the Fréchet differentiability of a nonlinear solution map from a bilinear control input to the solution of a Kirchhoff-type equation. We use this result to formulate the minimax optimal control problem. We show the existence of optimal pairs and find their necessary optimality conditions.http://dx.doi.org/10.1155/2019/3238462 |
| spellingShingle | Jin-soo Hwang Fréchet Differentiability for a Damped Kirchhoff-Type Equation and Its Application to Bilinear Minimax Optimal Control Problems International Journal of Differential Equations |
| title | Fréchet Differentiability for a Damped Kirchhoff-Type Equation and Its Application to Bilinear Minimax Optimal Control Problems |
| title_full | Fréchet Differentiability for a Damped Kirchhoff-Type Equation and Its Application to Bilinear Minimax Optimal Control Problems |
| title_fullStr | Fréchet Differentiability for a Damped Kirchhoff-Type Equation and Its Application to Bilinear Minimax Optimal Control Problems |
| title_full_unstemmed | Fréchet Differentiability for a Damped Kirchhoff-Type Equation and Its Application to Bilinear Minimax Optimal Control Problems |
| title_short | Fréchet Differentiability for a Damped Kirchhoff-Type Equation and Its Application to Bilinear Minimax Optimal Control Problems |
| title_sort | frechet differentiability for a damped kirchhoff type equation and its application to bilinear minimax optimal control problems |
| url | http://dx.doi.org/10.1155/2019/3238462 |
| work_keys_str_mv | AT jinsoohwang frechetdifferentiabilityforadampedkirchhofftypeequationanditsapplicationtobilinearminimaxoptimalcontrolproblems |