On Optimal Control of the Heat Flux at the Left-Hand Side in a Heat Conductivity System
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Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
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Yayıncı
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Optimal Control Problems, Heat Equation, Frechet Derivative, Adjoint Problem
Kaynak
Fundamentals of contemporary mathematical sciences (Online)
WoS Q Değeri
Scopus Q Değeri
Cilt
5
Sayı
1
