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Existence and uniqueness for an elliptic problem with evolution arising in electrodynamics

✍ Scribed by Micol Amar; Daniele Andreucci; Paolo Bisegna; Roberto Gianni

Book ID
103864238
Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
226 KB
Volume
6
Category
Article
ISSN
1468-1218

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✦ Synopsis

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 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.

Our mathematical scheme is of interest in the modelling of electrical conduction in biological tissues.

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