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Application of the \(j\)-subgradient in a problem of electropermeabilization. (English) Zbl 1516.35012

Summary: 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.

MSC:

35A15 Variational methods applied to PDEs
58J35 Heat and other parabolic equation methods for PDEs on manifolds
65N06 Finite difference methods for boundary value problems involving PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences

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Ipopt; FreeFem++
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References:

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