B. Ainseba, M. Bendahmane, and R. Ruiz-baier, Analysis of an optimal control problem for the tridomain model in cardiac electrophysiology, Journal of Mathematical Analysis and Applications, vol.388, issue.1, pp.231-247, 2012.
DOI : 10.1016/j.jmaa.2011.11.069

B. Andreianov, M. Bendahmane, K. H. Karlsen, and C. Pierre, Convergence of discrete duality finite volume schemes for the cardiac bidomain model. Networks and Heterogeneous Media, pp.195-240, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00526047

B. Andreianov, M. Bendahmane, A. Quarteroni, and R. Ruiz-baier, Solvability analysis and numerical approximation of linearized cardiac electromechanics, Mathematical Models and Methods in Applied Sciences, vol.25, issue.05, pp.25959-993, 2015.
DOI : 10.1142/S0218202515500244
URL : https://hal.archives-ouvertes.fr/hal-01256811

P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn et al., A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE, Computing, vol.24, issue.1, pp.121-138, 2008.
DOI : 10.1007/s00607-008-0004-9

M. Bendahmane and K. H. Karlsen, Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue. Networks and Heterogeneous Media, pp.185-218, 2006.

M. Blatt, A parallel algebraic multigrid method for elliptic problems with highly discontinuous coefficients, 2010.

Y. Bourgault, Y. Coudiére, and C. Pierre, Existence and uniqueness of the solution for the bidomain model used in cardiac electrophysiology, Nonlinear Analysis: Real World Applications, vol.10, issue.1, pp.458-482, 2009.
DOI : 10.1016/j.nonrwa.2007.10.007
URL : https://hal.archives-ouvertes.fr/hal-00101458

A. J. Brandao, E. Fernandez-cara, P. M. Magalhaes, and M. A. Rojas-medar, Theoretical analysis and control results for the fitzhugh-nagumo equation, Electronic Journal of Differential Equations (EJDE), issue.164, 2008.

H. Brezis, Analyse fonctionnelle, théorie et applications, 1983.

E. Casas, C. Ryll, and F. Tröltzsch, Sparse optimal control of the schlögl and fitzhugh-nagumo systems, Comput. Meth. in Appl. Math, vol.13, issue.4, pp.415-442, 2013.

N. Chamakuri and K. Kunisch, Primal-dual active set strategy for large scale optimization of cardiac defibrillation. submitted, 2015.

N. Chamakuri, K. Kunisch, and G. Plank, Numerical solution for optimal control of the reaction-diffusion equations in cardiac electrophysiology, Computational Optimization and Applications, vol.49, pp.149-178

N. Chamakuri, K. Kunisch, and G. Plank, Optimal control approach to termination of re-entry waves in cardiac electrophysiology, Journal of Mathematical Biology, pp.1-30

N. Chamakuri, K. Kunisch, and G. Plank, PDE constrained optimization of electrical defibrillation in a 3D ventricular slice geometry, International Journal for Numerical Methods in Biomedical Engineering, vol.59, issue.8, 2015.
DOI : 10.1007/s10589-009-9280-3

R. Fitzhugh, Impulses and Physiological States in Theoretical Models of Nerve Membrane, Biophysical Journal, vol.1, issue.6, pp.445-466, 1961.
DOI : 10.1016/S0006-3495(61)86902-6

P. C. Franzonea and G. Savaré, Degenerate Evolution Systems Modeling the Cardiac Electric Field at Micro- and Macroscopic Level, pp.49-78, 2006.
DOI : 10.1007/978-3-0348-8221-7_4

C. S. Henriquez, Simulating the electrical behavior of cardiac tissue using the bidomain model, Crit. Rev. Biomed. Eng, vol.21, pp.1-77, 1993.

D. A. Hooks, K. A. Tomlinson, S. G. Marsden, I. J. Legrice, B. H. Smaill et al., Cardiac Microstructure: Implications for Electrical Propagation and Defibrillation in the Heart, Circulation Research, vol.91, issue.4, pp.331-338, 2002.
DOI : 10.1161/01.RES.0000031957.70034.89

S. N. Kruzhkov, Results on the nature of the continuity of solutions of parabolic equations, and certain applications thereof, Mat. Zametki, vol.6, pp.97-108, 1969.

K. Kunisch and M. Wagner, Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions, ESAIM: Mathematical Modelling and Numerical Analysis, vol.47, issue.4, pp.1077-1106, 2013.
DOI : 10.1051/m2an/2012058

C. Mitchell and D. Schaeffer, A two-current model for the dynamics of cardiac membrane, Bulletin of Mathematical Biology, vol.65, issue.5, pp.767-793, 2003.
DOI : 10.1016/S0092-8240(03)00041-7

R. Plonsey, Bioelectric sources arising in excitable fibers (Alza lecture), Annals of Biomedical Engineering, vol.125, issue.6, pp.519-565, 1988.
DOI : 10.1007/BF02368014

B. J. Roth, Electrical conductivity values used with the bidomain model of cardiac tissue, IEEE Transactions on Biomedical Engineering, vol.44, issue.4, pp.326-328, 1997.
DOI : 10.1109/10.563303

L. Tung, A bi-domain model for describing ischemic myocardial DC potentials, 1978.

M. Veneroni, Reaction???diffusion systems for the macroscopic bidomain model of the cardiac electric field, Nonlinear Analysis: Real World Applications, vol.10, issue.2, pp.849-868, 2009.
DOI : 10.1016/j.nonrwa.2007.11.008