- Fundamentals of Contemporary Mathematical Sciences
- Cilt: 5 Sayı: 1
- On Optimal Control of the Heat Flux at the Left-Hand Side in a Heat Conductivity System
On Optimal Control of the Heat Flux at the Left-Hand Side in a Heat Conductivity System
Authors : Taha Koç, Yeşim Akbulut, Seher Aslanci
Pages : 15-24
Doi:10.54974/fcmathsci.1243111
View : 15 | Download : 19
Publication Date : 2024-01-31
Article Type : Research
Abstract :We deal with an optimal boundary control problem in a 1-d heat equation with Neumann boundary conditions. We search for a Neumann boundary function which is the minimum element of a quadratic cost functional involving the $H^1$-norm of boundary controls. We prove that the cost functional has a unique minimum element and is Frechet differentiable. We give a necessary condition for the optimal solution and construct a minimizing sequence using the gradient of the cost functional.Keywords : Optimal Control Problems, Heat Equation, Frechet Derivative, Adjoint Problem