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. (C) 2004 Elsevier Ltd. All rights reserved.
Existence and uniqueness for an elliptic problem with evolution arising in electrodynamics / GIANNI ROBERTO; ANDREUCCI DANIELE; MICOL AMAR; PAOLO BISEGNA. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - STAMPA. - 6:2(2005), pp. 367-380. [10.1016/j.nonrwa.2004.09.002]
Existence and uniqueness for an elliptic problem with evolution arising in electrodynamics
GIANNI ROBERTO;
2005
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. (C) 2004 Elsevier Ltd. All rights reserved.
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