On the Motion of a Compact Elastic Body

被引：0

作者：

Robert Beig

Michael Wernig-Pichler

机构：

[1] Universität Wien,Institut für Theoretische Physik der

来源：

Communications in Mathematical Physics | 2007年 / 271卷

关键词：

Killing Vector; Rigid Motion; Elastic Equation; Material Space; Strong Ellipticity;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations in material form (“Lagrangian coordinates”). By applying a basic theorem due to Koch, we prove short-time existence and uniqueness for solutions close to a trivial solution. This trivial, or natural, solution corresponds to a stress-free body in rigid motion.

引用

页码：455 / 465

页数：10

共 13 条

[1]

Beig R.(2003)Relativistic elasticity Class. Quantum Grav. 20 889-904

[2]

Schmidt B.G.(2002)A Riemannian version of Korn’s inequality Calc. Var. Partial Differ. Eq. 14 517-530

[3]

Chen W.(1992)Deformations of Incompressible Bodies with Free Boundaries Arch. Rat. Mech. Anal. 120 61-97

[4]

Jost J.(1995)Korn’s inequalities and their applications in continuum mechanics SIAM Rev. 37 491-511

[5]

Ebin D.(1976)Well-posed quasilinear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity Arch. Rat. Mech. Anal. 63 273-294

[6]

Horgan C.O.(1992)Relativistic elastomechanics as a Lagrangian field theory J. Geom. Phys. 9 207-223

[7]

Hughes T.(1993)Mixed problems for fully nonlinear hyperbolic equations Math. Z. 214 9-42

[8]

Kato T.(2005)Wellposedness for the motion of a compressible liquid with free surface boundary Commun. Math. Phys. 260 319-392

[9]

Marsden J.(undefined)undefined undefined undefined undefined-undefined

[10]

Kijowski J.(undefined)undefined undefined undefined undefined-undefined

← 1 2 →