International Journal of Differential Equations

On the Control of Coefficient Function in a Hyperbolic Problem with Dirichlet Conditions

Seda İğret Araz and Murat Subaşi

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Abstract

This paper presents theoretical results about control of the coefficient function in a hyperbolic problem with Dirichlet conditions. The existence and uniqueness of the optimal solution for optimal control problem are proved and adjoint problem is used to obtain gradient of the functional. However, a second adjoint problem is given to calculate the gradient on the space W210,l. After calculating gradient of the cost functional and proving the Lipschitz continuity of the gradient, necessary condition for optimal solution is constructed.

Article information

Source
Int. J. Differ. Equ., Volume 2018, Special Issue (2018), Article ID 7417590, 6 pages.

Dates
Received: 6 February 2018
Revised: 2 April 2018
Accepted: 4 April 2018
First available in Project Euclid: 10 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1539136980

Digital Object Identifier
doi:10.1155/2018/7417590

Mathematical Reviews number (MathSciNet)
MR3861847

Citation

İğret Araz, Seda; Subaşi, Murat. On the Control of Coefficient Function in a Hyperbolic Problem with Dirichlet Conditions. Int. J. Differ. Equ. 2018, Special Issue (2018), Article ID 7417590, 6 pages. doi:10.1155/2018/7417590. https://projecteuclid.org/euclid.ijde/1539136980


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