On Optimal Control of the Heat Flux at the Left-Hand Side in a Heat Conductivity System

Year 2024, Volume: 5 Issue: 1, 15 - 24, 31.01.2024

Taha Koç , Yeşim Akbulut , Seher Aslancı

https://doi.org/10.54974/fcmathsci.1243111

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

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