We study the existence and uniqueness of solutions to an elliptic problem with a nonlinear dynamic boundary condition, relating the conormal derivative of the unknown to the time derivative of its jump across an intemal interface. We firstly prove the well-posedness of a suitable linear version of this problem, by means of a classical result in abstract parabolic theory; then, we study the nonlinear case using a fixed point technique. Our mathematical scheme is of interest in the modelling of electrical conduction in biological tissues.
Amar, M., Andreucci, D., Bisegna, P., Gianni, R. (2005). Existence and uniqueness for an elliptic problem with evolution arising in electrodynamics. NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS, 6(2), 367-380 [10.1016/j.nonrwa.2004.09.002].
Existence and uniqueness for an elliptic problem with evolution arising in electrodynamics
BISEGNA, PAOLO;
2005-01-01
Abstract
We study the existence and uniqueness of solutions to an elliptic problem with a nonlinear dynamic boundary condition, relating the conormal derivative of the unknown to the time derivative of its jump across an intemal interface. We firstly prove the well-posedness of a suitable linear version of this problem, by means of a classical result in abstract parabolic theory; then, we study the nonlinear case using a fixed point technique. Our mathematical scheme is of interest in the modelling of electrical conduction in biological tissues.| File | Dimensione | Formato | |
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