On the optimal control problem for Schrodinger equation with complex potential
Yükleniyor...
Tarih
2010
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier Science Inc
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The existence and uniqueness for the solution of the problem of determining the v(x, t) potential in the Schrodinger equation i partial derivative psi/partial derivative t + partial derivative/partial derivative x (a(0)(x)partial derivative psi/partial derivative x) - a(x)psi + iv(x, t)psi = f(x, t) from the measured final data psi(x,T) = y(x) is investigated. For the objective functional J(alpha)(nu) = parallel to psi(x, T; v) - y(x)parallel to(2)(L2)(0,l) + alpha parallel to nu - w parallel to(2)(W2)0,1 (Omega), it is proven that the problem has at least one solution for a alpha >= 0, and has a unique solution for alpha > 0. The necessary condition for solvability the problem is stated as the variational principle. (C) 2010 Elsevier Inc. All rights reserved.
Açıklama
Anahtar Kelimeler
Optimal control problem, Schrodinger equation, Frechet differential
Kaynak
Applied Mathematics and Computation
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
216
Sayı
7
