A CLASS OF PARABOLIC EQUATIONS DRIVEN BY THE MEAN CURVATURE FLOW

被引：0

作者：

de Araujo, Anderson L. A. ^{[1
]}

Montenegro, Marcelo ^{[2
]}

机构：

[1] Univ Fed Vicosa, CCE, Dept Matemat, Ave PH Rolfs S-N, BR-36570900 Vicosa, MG, Brazil

[2] Univ Estadual Campinas, IMECC, Dept Matemat, Rua Sergio Buarque Holanda 651, BR-13083859 Campinas, SP, Brazil

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2019年 / 62卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

mean curvature flow; asymptotic behaviour; stability; ASYMPTOTIC-BEHAVIOR; SINGULARITIES; SURFACES; CURVES; EVOLUTION;

D O I：

10.1017/S001309151800038X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a class of parabolic equations which can be viewed as a generalized mean curvature flow acting on cylindrically symmetric surfaces with a Dirichlet condition on the boundary. We prove the existence of a unique solution by means of an approximation scheme. We also develop the theory of asymptotic stability for solutions of general parabolic problems.

引用

页码：135 / 163

页数：29

共 24 条

[1] Mean curvature flow through singularities for surfaces of rotation [J].

Altschuler, S ;

Angenent, SB ;

Giga, Y .

JOURNAL OF GEOMETRIC ANALYSIS, 1995, 5 (03) :293-358

[2]

ANGENENT S, 1991, J DIFFER GEOM, V33, P601

[3] PARABOLIC EQUATIONS FOR CURVES ON SURFACES .2. INTERSECTIONS, BLOW-UP AND GENERALIZED SOLUTIONS [J].

ANGENENT, S .

ANNALS OF MATHEMATICS, 1991, 133 (01) :171-215

[4] PARABOLIC EQUATIONS FOR CURVES ON SURFACES .1. CURVES WITH P-INTEGRABLE CURVATURE [J].

ANGENENT, S .

ANNALS OF MATHEMATICS, 1990, 132 (03) :451-483

[5] ON ROTATIONALLY SYMMETRICAL MEAN-CURVATURE FLOW [J].

DZIUK, G ;

KAWOHL, B .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1991, 93 (01) :142-149

[6]

Escher J., 2010, ANALYSIS, V30, P253

[7] MOTION OF LEVEL SETS BY MEAN-CURVATURE .2. [J].

EVANS, LC ;

SPRUCK, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 330 (01) :321-332

[8]

FILA M, 1992, COMMUN PART DIFF EQ, V17, P593

[9]

Friedman A., 1964, Partial differential equations of the parabolic type

[10]

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

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