BOUNDARY FEEDBACK STABILIZATION OF THE MONODOMAIN EQUATIONS

摘要

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.