Abels, Helmut and Lam, Kei Fong and Stinner, Bjoern (2015) ANALYSIS OF THE DIFFUSE DOMAIN APPROACH FOR A BULK-SURFACE COUPLED PDE SYSTEM. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 47 (5). pp. 3687-3725. ISSN 0036-1410, 1095-7154
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We analyze a diffuse interface type approximation, known as the diffuse domain approach, of a linear coupled bulk-surface elliptic 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | COMPLEX GEOMETRIES; INTERFACE APPROACH; SOLUBLE SURFACTANTS; SOLVING PDES; 2-PHASE FLOW; ASYMPTOTICS; ADVECTION; diffuse domain method; weighted Sobolev spaces; well-posedness; diffuse interface approximation; asymptotic analysis; bulk-surface elliptic equations |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 26 Jul 2019 10:02 |
| Last Modified: | 26 Jul 2019 10:02 |
| URI: | https://pred.uni-regensburg.de/id/eprint/6158 |
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