Finite element approximation of sparse parabolic control problems
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Quantification of the unique continuation property for the heat equation
September 2017, 7(3): 369-391. doi: 10.3934/mcrf.2017013
Boundary feedback stabilization of the monodomain equations
Tobias Breiten 1,, and Karl Kunisch 1,2,
Institute for Mathematics and Scientific Computing, Karl-Franzens-Universität Graz, Heinrichstr. 36,8010 Graz, Austria
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstraße 69, A-4040 Linz, Austria
* Corresponding author: Tobias Breiten
Received July 2016 Revised November 2016 Published July 2017
Figure(4)
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.
Keywords: Boundary control, feedback stabilization, reaction diffusion system, algebraic Riccati equation.
Mathematics Subject Classification: Primary: 35K57, 93D15, 93B52.
Citation: Tobias Breiten, Karl Kunisch. Boundary feedback stabilization of the monodomain equations. Mathematical Control & Related Fields, 2017, 7 (3) : 369-391. doi: 10.3934/mcrf.2017013
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Figure 1. Control setup
Figure 2. Stabilization of perturbed initial state
Figure 3. Stabilization of a reentry wave
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