NONLOCAL SPATIALLY INHOMOGENEOUS HAMILTON-JACOBI EQUATION WITH UNUSUAL FREE BOUNDARY

被引：6

作者：

Giga, Yoshikazu ^{[1
]}

Gorka, Przemyslaw ^{[2
,3
]}

Rybka, Piotr ^{[4
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Tokyo 1538914, Japan

[2] Univ Talca, Inst Matemat & Fis, Talca, Chile

[3] Warsaw Univ Technol, Dept Math & Informat Sci, PL-00661 Warsaw, Poland

[4] Univ Warsaw, Inst Appl Math & Mech, PL-07097 Warsaw, Poland

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 26卷 / 02期

基金：

日本学术振兴会;

关键词：

driven curvature flow; singular energies; Hamilton-Jacobi equation; free boundary; discontinuous Hamiltonian; comparison principle; VISCOSITY SOLUTIONS; CRYSTALLINE CURVATURE; DRIVEN; FACETS;

D O I：

10.3934/dcds.2010.26.493

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the weighted mean curvature flow in the plane with a driving term. For certain anisotropy functions this evolution problem degenerates to a first order Hamilton-Jacobi equation with a free boundary. The resulting problem may be written as a Hamilton-Jacobi equation with a spatially non-local and discontinuous Hamiltonian. We prove existence and uniqueness of solutions. On the way we show a comparison principle and a stability theorem for viscosity solutions.

引用

页码：493 / 519

页数：27

共 28 条

[1]

[Anonymous], DIFFERENTIAL INTEGRA

[2]

[Anonymous], WORLD C NONL AN 92

[3]

Bardi M., 1997, Optimal control and viscosity solutions of HamiltonJacobi-Bellman equations

[4]

BARLES G, 1987, ESAIM-MATH MODEL NUM, V21, P557

[5]

Barles G., 1994, Mathematiques & Applications (Berlin) Mathematics & Applications, V17

[6]

Bellettini G, 2001, ARCH RATION MECH AN, V157, P193, DOI 10.1007/s002050100127

[7]

Bellettini G., 2000, Adv. Math. Sci. Appl, V10, P467

[8]

Bellettini G., 2001, Interfaces Free Bound., V3, P415, DOI [10.4171/IFB/47, DOI 10.4171/IFB/47]

[9] Time-dependent measurable Hamilton-Jacobi equations [J].

Camilli, F ;

Siconolfi, A .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2005, 30 (4-6) :813-847

[10] A characterization of convex calibrable sets in RN with respect to anisotropic norms [J].

Caselles, V. ;

Chambolle, A. ;

Moll, S. ;

Novaga, M. .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2008, 25 (04) :803-832

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