Application of the j-Subgradient in a Problem of Electropermeabilization
Copyright policy )Application of the j-Subgradient in a Problem of Electropermeabilization
We study a coupled elliptic-parabolic Poincaré-Steklov system arising in electrical cell activity in biological tissues. By using the notion of $j$-subgradient, we show that this system has a gradient structure and thus obtain wellposedness. We further exploit the gradient structure for the discretisation of the problem and provide numerical experiments.
19 pages
Finite difference methods for boundary value problems involving PDEs, \(j\)-subgradient, PDEs in connection with biology, chemistry and other natural sciences, electropermeabilization, [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], Heat and other parabolic equation methods for PDEs on manifolds, Numerical Analysis (math.NA), Variational methods applied to PDEs, Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Steklov-Poincaré operator, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Primary: 35K55, 37L05, 47H05 Secondary: 35R01, 35A15, 65N30, Analysis of PDEs (math.AP)
Finite difference methods for boundary value problems involving PDEs, \(j\)-subgradient, PDEs in connection with biology, chemistry and other natural sciences, electropermeabilization, [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], Heat and other parabolic equation methods for PDEs on manifolds, Numerical Analysis (math.NA), Variational methods applied to PDEs, Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Steklov-Poincaré operator, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Primary: 35K55, 37L05, 47H05 Secondary: 35R01, 35A15, 65N30, Analysis of PDEs (math.AP)
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