Quadratic Cost Minimax Optimal Control Problems for a Semilinear Viscoelastic Equation with Long Memory
In this paper, we study the quadratic cost minimax optimal control problems for a semilinear viscoelastic equation with long memory. A global well-posedness theorem regarding the solutions to its Cauchy problem is given. We formulate the minimax control problem with bilinear control inputs and corre...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6689119 |
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| _version_ | 1832546839647223808 |
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| author | Jin-soo Hwang |
| author_facet | Jin-soo Hwang |
| author_sort | Jin-soo Hwang |
| collection | DOAJ |
| description | In this paper, we study the quadratic cost minimax optimal control problems for a semilinear viscoelastic equation with long memory. A global well-posedness theorem regarding the solutions to its Cauchy problem is given. We formulate the minimax control problem with bilinear control inputs and corresponding disturbances. Under some assumptions, we prove the existence of optimal pairs and give necessary optimality conditions for optimal pairs in some observation cases. |
| format | Article |
| id | doaj-art-d8f317b31cfe4f5f93875bcc848bc548 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d8f317b31cfe4f5f93875bcc848bc5482025-02-03T06:47:03ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66891196689119Quadratic Cost Minimax Optimal Control Problems for a Semilinear Viscoelastic Equation with Long MemoryJin-soo Hwang0Department of Mathematics Education, College of Education, Daegu University, Jillyang, Gyeongsan, Gyeongbuk, Republic of KoreaIn this paper, we study the quadratic cost minimax optimal control problems for a semilinear viscoelastic equation with long memory. A global well-posedness theorem regarding the solutions to its Cauchy problem is given. We formulate the minimax control problem with bilinear control inputs and corresponding disturbances. Under some assumptions, we prove the existence of optimal pairs and give necessary optimality conditions for optimal pairs in some observation cases.http://dx.doi.org/10.1155/2021/6689119 |
| spellingShingle | Jin-soo Hwang Quadratic Cost Minimax Optimal Control Problems for a Semilinear Viscoelastic Equation with Long Memory Journal of Mathematics |
| title | Quadratic Cost Minimax Optimal Control Problems for a Semilinear Viscoelastic Equation with Long Memory |
| title_full | Quadratic Cost Minimax Optimal Control Problems for a Semilinear Viscoelastic Equation with Long Memory |
| title_fullStr | Quadratic Cost Minimax Optimal Control Problems for a Semilinear Viscoelastic Equation with Long Memory |
| title_full_unstemmed | Quadratic Cost Minimax Optimal Control Problems for a Semilinear Viscoelastic Equation with Long Memory |
| title_short | Quadratic Cost Minimax Optimal Control Problems for a Semilinear Viscoelastic Equation with Long Memory |
| title_sort | quadratic cost minimax optimal control problems for a semilinear viscoelastic equation with long memory |
| url | http://dx.doi.org/10.1155/2021/6689119 |
| work_keys_str_mv | AT jinsoohwang quadraticcostminimaxoptimalcontrolproblemsforasemilinearviscoelasticequationwithlongmemory |