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K. D. Phung, G. Wang and X. Zhang, “On the Existence of Time Optimal Controls for Linear Evolution Equations,” Discrete and Continuous Dynamical Systems, Series B, Vol. 8, No. 4, 2007, pp. 925-941.
http://dx.doi.org/10.3934/dcdsb.2007.8.925

has been cited by the following article:

• TITLE: Time-Optimal Control Problem for n× n Co-Operative Parabolic Systems with Control in Initial Conditions

  AUTHORS: Mohammed A. Shehata

  KEYWORDS: Time-Optimal Control Problems; Bang-Bang Controls; Parabolic System; Co-Operative Systems

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.9A, December 31, 2013

  ABSTRACT: In this paper, time-optimal control problem for a liner n× n co-operative parabolic system involving Laplace operator is considered. This problem is, steering an initial state y(0)=u, with control uso that an observation y(t) hitting a given target set in minimum time. First, the existence and uniqueness of solutions of such system under conditions on the coefficients are proved. Afterwards necessary and sufficient conditions of optimality are obtained. Finally a scaler case is given.