T. Nambu, “An L2(Ω)-Based Algebraic Approach to Boundary Stabilization for Linear Parabolic Systems,” Quarterly of Applied Mathematics, Vol. 62, No. 4, 2004, pp. 711-748.

has been cited by the following article:

• TITLE: On Decay of Solutions and Spectral Property for a Class of Linear Parabolic Feedback Control Systems

  AUTHORS: Takao Nambu

  KEYWORDS: Stabilization of Linear Parabolic Systems; Decay of Functionals; Dynamic Feedback Scheme; Spectral Structures of Composite Systems; Complete Observability of Systems

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.9A, December 18, 2013

  ABSTRACT: Unlike regular stabilizations, we construct in the paper a specific feedback control system such that u(t) decays exponentially with the designated decay rate, and that some non-trivial linear functionals of u decay exactly faster than . The system contains a dynamic compensator with another state v in the feedback loop, and consists of two states u and v. This problem entirely differs from the one with static feedback scheme in which the system consists only of a single state u. To show the essential difference, some specific property of the spectral subspaces associated with our control system is studied.