Inserted: 16 jul 2003
Last Updated: 4 mar 2005
Journal: Nonlinear Analysis - Real Word Applications
We study the existence and uniqueness for 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 internal 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.
\noindent Our mathematical scheme is of interest in the modelling of electrical conduction in biological tissues.