A center manifold analysis for the Mullins-Sekerka model

被引：100

作者：

Escher, J ^{[1
]}

Simonett, G

机构：

[1] Univ Basel, Inst Math, CH-4051 Basel, Switzerland

[2] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 1998年 / 143卷 / 02期

关键词：

Mullins-Sekerka model; mean curvature; free boundary problem; generalized motion by mean curvature; center manifold;

D O I：

10.1006/jdeq.1997.3373

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Mullins-Sekerka model is a nonlocal evolution model for hypersurfaces, which arises as a singular limit for the Cahn-Hilliard equation. We show that classical solutions exist globally and tend to spheres exponentially fast, provided that they are close to a sphere initially. Our analysis is based on center manifold theory and on maximal regularity. (C) 1998 Academic Press.

引用

页码：267 / 292

页数：26

共 38 条

[21]

Escher J., 1997, ADV DIFFERENTIAL EQU, V2, P619

[22]

Escher J, 1996, MATH RES LETT, V3, P467

[23]

GAGE M, 1986, J DIFFER GEOM, V23, P69

[24]

Gurtin M.E., 1993, Thermomechanics of evolving phase boundaries in the plane Clarendon Press

[25]

Oxford University Press

[26] CLASSICAL-SOLUTIONS OF THE STEFAN PROBLEM [J].

HANZAWA, EI .

TOHOKU MATHEMATICAL JOURNAL, 1981, 33 (03) :297-335

[27] On the second eigenvalue of the Laplace operator penalized by curvature [J].

Harrell, EM .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 1996, 6 (04) :397-400

[28]

HUISKEN G, 1984, J DIFFER GEOM, V20, P237

[29]

Lunardi A., 1995, ANAL SEMIGROUPS OPTI

[30]

MAYER UF, 1993, ELECT J DIFFERENTIAL, P1

← 1 2 3 4 →