Koç, TahaSaraç, YeşimAslancı, Seher2026-01-242026-01-2420242717-6185https://search.trdizin.gov.tr/tr/yayin/detay/1225648https://doi.org/10.54974/fcmathsci.1243111https://hdl.handle.net/20.500.12868/4018We 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.eninfo:eu-repo/semantics/openAccessOptimal Control ProblemsHeat EquationFrechet DerivativeAdjoint ProblemArticle10.54974/fcmathsci.12431115115241225648