Degenerate Evolution Systems Modeling the Cardiac Electric Field at Micro- and Macroscopic Level

[1]  Federico Bassetti,et al.  Variable Time-Step Discretization of Degenerate Evolution Equations in Banach Spaces , 2003 .

[2]  S. Sanfelici.  Convergence of the Galerkin approximation of a degenerate evolution problem in electrocardiology , 2002 .

[3]  Giuseppe Savare',et al.  A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations † , 2000 .

[4]  N. Trayanova,et al.  The role of cardiac tissue structure in defibrillation. , 1998, Chaos.

[5]  W. Krassowska,et al.  The induction of reentry in cardiac tissue. The missing link: How electric fields alter transmembrane potential. , 1998, Chaos.

[6]  Angelo Favini,et al.  Degenerate differential equations in Banach spaces , 1998 .

[7]  R. Showalter.  Monotone operators in Banach space and nonlinear partial differential equations , 1996 .

[8]  C. Henriquez,et al.  Anisotropy, Fiber Curvature, and Bath Loading Effects on Activation in Thin and Thick Cardiac Tissue Preparations: , 1996, Journal of cardiovascular electrophysiology.

[9]  J. Rulla,et al.  Error analysis for implicit approximations to solutions to Cauchy problems , 1996 .

[10]  C. Luo,et al.  A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. , 1994, Circulation research.

[11]  P. C. Franzone,et al.  Spreading of excitation in 3-D models of the anisotropic cardiac tissue. I. Validation of the eikonal model. , 1993, Mathematical biosciences.

[12]  Michael Mascagni,et al.  The backward Euler method for numerical solution of the Hodgkin-Huxley equations of nerve conduction , 1990 .

[13]  N. Britton.  Reaction-diffusion equations and their applications to biology. , 1989 .

[14]  R. Showalter,et al.  Implicit Degenerate Evolution Equations and Applications , 1981 .

[15]  E. Johnson,et al.  Fast sodium current in cardiac muscle. A quantitative description. , 1980, Biophysical journal.

[16]  E. Sanchez-Palencia.  Non-Homogeneous Media and Vibration Theory , 1980 .

[17]  Joseph W. Jerome,et al.  Convergence of Successive Iterative Semidiscretizations for Fitzhugh–Nagumo Reaction Diffusion Systems , 1980 .

[18]  A. Bensoussan,et al.  Asymptotic analysis for periodic structures , 1979 .

[19]  David Hoff,et al.  Stability and Convergence of Finite Difference Methods for Systems of Nonlinear Reaction-Diffusion Equations , 1978 .

[20]  H. Brezis.  Integrales convexes dans les espaces de Sobolev , 1972 .

[21]  E. Boschi.  Recensioni: J. L. Lions - Quelques méthodes de résolution des problémes aux limites non linéaires. Dunod, Gauthier-Vi;;ars, Paris, 1969; , 1971 .

[22]  H. Brezis,et al.  Sur une classe de problèmes d'évolution non linéaires , 1969 .

[23]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[24]  J. Lions.  Quelques méthodes de résolution de problèmes aux limites non linéaires , 2017 .

[25]  James P. Keener,et al.  Mathematical physiology , 1998 .

[26]  V. Zhikov,et al.  Homogenization of Differential Operators and Integral Functionals , 1994 .

[27]  C. Henriquez.  Simulating the electrical behavior of cardiac tissue using the bidomain model. , 1993, Critical reviews in biomedical engineering.

[28]  W. Krassowska,et al.  Homogenization of syncytial tissues. , 1993, Critical reviews in biomedical engineering.

[29]  B. Roth,et al.  How the anisotropy of the intracellular and extracellular conductivities influences stimulation of cardiac muscle , 1992, Journal of mathematical biology.

[30]  P. C. Franzone,et al.  Wavefront propagation in an activation model of the anisotropic cardiac tissue: asymptotic analysis and numerical simulations , 1990, Journal of mathematical biology.

[31]  A. Visintin,et al.  On A Class Of Doubly Nonlinear Evolution Equations , 1990 .

[32]  Claudio Baiocchi,et al.  Discretization of Evolution Variational Inequalities , 1989 .

[33]  N. Bakhvalov,et al.  Homogenisation: Averaging Processes in Periodic Media: Mathematical Problems in the Mechanics of Composite Materials , 1989 .

[34]  H. Attouch.  Variational convergence for functions and operators , 1984 .

[35]  J. Smoller.  Shock Waves and Reaction-Diffusion Equations , 1983 .

[36]  Robert M. Miura,et al.  Accurate computation of the stable solitary wave for the FitzHugh-Nagumo equations , 1982 .

[37]  R. Glowinski,et al.  Numerical Analysis of Variational Inequalities , 1981 .

[38]  J. Cronin.  Mathematics of cell electrophysiology , 1981 .

[39]  Ralph E. Showalter,et al.  Singular and degenerate Cauchy problems , 1976 .

[40]  R. G. Casten,et al.  Perturbation analysis of an approximation to the Hodgkin-Huxley theory , 1975 .

[41]  J. Jack,et al.  Electric current flow in excitable cells , 1975 .

[42]  H. Brezis.  Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert , 1973 .

[43]  Haim Brezis,et al.  Monotonicity Methods in Hilbert Spaces and Some Applications to Nonlinear Partial Differential Equations , 1971 .