Name
Abstract | ||
|---|---|---|
We study coarsening of a binary mixture within the Mullins-Sekerka evolution in the regime where one phase has small volume fraction phi << 1. Heuristic arguments suggest that the energy density, which represents the inverse of a typical length scale, decreases as phi t(-1/3) as t ->infinity. We prove rigorously a corresponding weak lower bound. Moreover, we establish a stronger result for the two-dimensional case, where we find a lower bound of the form phi(ln phi(-1))(1/3)t(-1/3). Our approach follows closely the analysis in [R.V. Kohn and F. Otto, Comm. Math. Phys., 229 (2002), pp. 375-395], which exploits the relation between two suitable length scales. Our main contribution is an isoperimetric inequality in the two-dimensional case. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1137/040620059 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
Mullins-Sekerka evolution,coarsening rates,isoperimetric inequalities | Inverse,Combinatorics,Length scale,Mathematical analysis,Upper and lower bounds,Energy density,Isoperimetric inequality,Mathematics,Binary number | Journal |
Volume | Issue | ISSN |
37 | 6 | 0036-1410 |
Citations | PageRank | References |
5 | 1.15 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| SERGIO CONTI | 1 | 6 | 2.02 |
| BARBARA NIETHAMMER | 2 | 15 | 5.87 |
| FELIX OTTOz | 3 | 5 | 1.15 |