On an elasto-dynamic evolution equation with non dead load and friction

被引：0
作者：
Chau O. [1 ]
机构：
[1] Faculté des Sciences et Technologies, Département de Mathématiques et Informatiques, Université de la Réunion, 97715 Saint-Denis Messag Cedex 9, La Réunion
来源：
Applications of Mathematics | 2006年 / 51卷 / 3期
关键词：
dynamic process; elasticity; evolution equation; existence xxx uniqueness; Faedo-Galerkin method; friction;
D O I：
10.1007/s10492-006-0013-y
中图分类号：
学科分类号：
摘要：
In this paper, we are interested in the dynamic evolution of an elastic body, acted by resistance forces depending also on the displacements. We put the mechanical problem into an abstract functional framework, involving a second order nonlinear evolution equation with initial conditions. After specifying convenient hypotheses on the data, we prove an existence and uniqueness result. The proof is based on Faedo-Galerkin method. © 2006 Springer Science+Business Media, Inc.
引用
收藏
页码：229 / 246
页数：17
相关论文
共 20 条
  • [1] Barbu V., Nonlinear Semigroups and Differential Equations in Banach Spaces, (1976)
  • [2] Brezis H., Analyse fonctionnelle, Théorie et Application, (1983)
  • [3] Browder F.E., On non-linear wave equations, Math. Z., 80, pp. 249-264, (1962)
  • [4] Cazenave T., Haraux A., An Introduction to Semilinear Evolution Equations, (1998)
  • [5] Chau O., Fernandez J.R., Han W., Sofonea M., Variational and numerical analysis of a dynamic frictionless contact problem with adhesion, J. Comput. Appl. Math., 156, pp. 127-157, (2003)
  • [6] Ciarlet P.G., Mathematical Elasticity, Vol. I: Three-dimmensional Elasticity, (1988)
  • [7] Dautray R., Lions J.-L., Mathematical Analysis and Numerical Methods for Science and Technology, Tome 5, (2000)
  • [8] Duvaut G., Lions J.-L., Inequalities in Mechanics and Physics, (1976)
  • [9] Jarusek J., Dynamic contact problems with given friction for viscoelastic bodies, Czech. Math. J., 46, 121, pp. 475-487, (1996)
  • [10] Jarusek J., Eck C., Dynamic contact problems with small Coulomb friction for viscoelastic bodies. Existence of solutions, Math. Models Methods Appl. Sci., 9, pp. 11-34, (1999)
12