The Library
Analysis of the diffuse domain approach for a bulk-surface coupled PDE system
Tools
Abels, Abels, Lam, Kei Fong and Stinner, Björn (2015) Analysis of the diffuse domain approach for a bulk-surface coupled PDE system. SIAM Journal on Mathematical Analysis, 47 (5). pp. 3687-3725. doi:10.1137/15M1009093 ISSN 0036-1410.
|
PDF
WRAP_RevisedALSDiffuseDomainBulkSurface15.pdf - Accepted Version - Requires a PDF viewer. Download (833Kb) | Preview |
Official URL: http://dx.doi.org/10.1137/15M1009093
Abstract
We analyse a diffuse interface type approximation, known as the diffuse domain approach, of a linear coupled bulk-surface elliptic \textcolor{blue}{PDE} system. The well-posedness of the diffuse domain approximation is shown using weighted Sobolev spaces and we prove that the solution to the diffuse domain approximation converges weakly to the solution of the coupled bulk-surface elliptic system as the approximation parameter tends to zero. Moreover, we can show strong convergence for the bulk quantity, while for the surface quantity, we can show norm convergence and strong convergence in a weighted Sobolev space. %Our analysis also covers a second order surface elliptic partial differential equation and a bulk elliptic partial differential equation with Dirichlet, Neumann and Robin boundary condition.
Item Type: | Journal Article | ||||||||
---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Differential equations, Partial -- Research, Differential equations, Elliptic, Sobolev spaces | ||||||||
Journal or Publication Title: | SIAM Journal on Mathematical Analysis | ||||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||||
ISSN: | 0036-1410 | ||||||||
Official Date: | 1 October 2015 | ||||||||
Dates: |
|
||||||||
Volume: | 47 | ||||||||
Number: | 5 | ||||||||
Page Range: | pp. 3687-3725 | ||||||||
DOI: | 10.1137/15M1009093 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 2 June 2016 | ||||||||
Date of first compliant Open Access: | 3 June 2016 | ||||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
Grant number: | EP/H023364/1 | ||||||||
Adapted As: | |||||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year