On the optimal coefficient control in a heat equation

Seda İǧret Araz, ,Siirt University, Department of Mathematics Education, Siirt, Turkey, Murat Subașı, ,Ataturk University, Science Faculty, Department of Mathematics, Erzurum, Turkey
2018 Discrete and Continuous Dynamical Systems. Series S  
In this study, optimal control of a senior coefficient in a heat conduction problem is discussed. Since such problems are severely ill-posed, it is necessary to regularize them. So, we present the regularization process which has a great importance for a optimal control problem in this study. After proving the existence and uniqueness of optimal solution, a necessary condition for optimality is stated. Then, an iterative algorithm is purposed for numerical approximations. Finally, optimal
more » ... l has been approximately calculated using the obtained results. The outcomes have also been tested with numerical examples. 2010 Mathematics Subject Classification. 34K35, 47A52, 80A20.
doi:10.3934/dcdss.2020124 fatcat:dcfleu4a6neathapsxclgymu2e