Affiliation:
1. ATATÜRK ÜNİVERSİTESİ
2. ALANYA ALAADDİN KEYKUBAT ÜNİVERSİTESİ
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.
Publisher
Fundamentals of Contemporary Mathematical Sciences
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