Boundary Feedback Stabilization of an Unstable Heat Equation

@article{Liu2003BoundaryFS,
  title={Boundary Feedback Stabilization of an Unstable Heat Equation},
  author={Weijiu Liu},
  journal={SIAM J. Control and Optimization},
  year={2003},
  volume={42},
  pages={1033-1043}
}
In this paper we study the problem of boundary feedback stabilization for the unstable heat equation ut(x,t) = uxx(x,t)+a(x) u(x,t). This equation can be viewed as a model of a heat conducting rod in which not only is the heat being diffused (mathematically due to the diffusive term uxx) but also the destabilizing heat is generating (mathematically due to the term a u with a >0). We show that for any given continuously differentiable function a and any given positive constant $\l$ we can… CONTINUE READING

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Infinite-step backstepping for a heat equation-like PDE with arbitrarily many unstable eigenvalues

  • Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148)
  • 2001
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL