Optimal control for obstacle problems involving time-dependent variational inequalities with Liouville–Caputo fractional derivative
| Autor: | Apassara Suechoei, Parinya Sa Ngiamsunthorn, Poom Kumam |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Algebra and Number Theory
Partial differential equation Applied Mathematics Fractional calculus Optimal control 01 natural sciences Existence of solutions 010101 applied mathematics Obstacle problems Obstacle Norm (mathematics) Ordinary differential equation 0103 physical sciences Obstacle problem Variational inequality QA1-939 Applied mathematics 0101 mathematics 010306 general physics Analysis Mathematics |
| Zdroj: | Advances in Difference Equations, Vol 2021, Iss 1, Pp 1-18 (2021) |
| ISSN: | 1687-1847 |
| Popis: | We consider an optimal control problem for a time-dependent obstacle variational inequality involving fractional Liouville–Caputo derivative. The obstacle is considered as the control, and the corresponding solution to the obstacle problem is regarded as the state. Our aim is to find the optimal control with the properties that the state is closed to a given target profile and the obstacle is not excessively large in terms of its norm. We prove existence results and establish necessary conditions of obstacle problems via the approximated time fractional-order partial differential equations and their adjoint problems. The result in this paper is a generalization of the obstacle problem for a parabolic variational inequalities as the Liouville–Caputo fractional derivatives were used instead of the classical derivatives. |
| Databáze: | OpenAIRE |
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