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Boundary feedback stabilization of the monodomain equations

  • * Corresponding author: Tobias Breiten

    * Corresponding author: Tobias Breiten 
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  • Boundary feedback control for a coupled nonlinear PDE-ODE system (in the two and three dimensional cases) is studied. Particular focus is put on the monodomain equations arising in the context of cardiac electrophysiology. Neumann as well as Dirichlet based boundary control laws are obtained by an algebraic operator Riccati equation associated with the linearized system. Local exponential stability of the nonlinear closed loop system is shown by a fixed-point argument. Numerical examples are given for a finite element discretization of the two dimensional monodomain equations.

    Mathematics Subject Classification: Primary: 35K57, 93D15, 93B52.

    Citation:

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  • Figure 1.  Control setup

    Figure 2.  Stabilization of perturbed initial state

    Figure 3.  Stabilization of a reentry wave

    Figure 4.  Stabilization of perturbed initial state

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