Title
A Transmission Problem Across a Fractal Self-Similar Interface
Abstract
AbstractWe consider a transmission problem in which the interior domain has infinitely ramified structures.Transmission between the interior and exterior domains occurs only at the fractal component of the interface between the interior and exterior domains.We also consider the sequence of the transmission problems in which the interior domain is obtained by stopping the self-similar construction after a finite number of steps;the transmission condition is then posed on a prefractal approximation of the fractal interface. We prove the convergence in the sense of Mosco of the energy forms associated with these problems to the energy form of the limit problem. In particular, this implies the convergence of the solutions of the approximated problems tothe solution of the problem with fractal interface. The proof relies in particular on an extension property.Emphasis is put on the geometry of the ramified domain. The convergence result is obtained when the fractal interface has no self-contact, and in a particular geometry with self-contacts, for which an extension result is proved.
Year
DOI
Venue
2016
10.1137/15M1029497
Periodicals
Keywords
Field
DocType
transmission problems,Gamma-convergence,extension theorems
Convergence (routing),Mathematical optimization,Finite set,Mathematical analysis,Fractal,Mathematics,Ramification
Journal
Volume
Issue
ISSN
14
2
1540-3459
Citations 
PageRank 
References 
0
0.34
3
Authors
2
Name
Order
Citations
PageRank
Yves Achdou119732.74
thibaut deheuvels200.34