Existence and uniqueness for dynamical unilateral contact with Coulomb friction: a model problem
Existence and uniqueness for dynamical unilateral contact with Coulomb friction: a model problem
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DOI：
10.1051/m2an:2005004
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
P. Ballard;S. Basseville
中科院分区：
文献类型：
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作者：
P. Ballard;S. Basseville
考虑了一个简单的库仑型单侧接触干摩擦动力学问题的原型。研究一类具有柯西数据的系统解的存在唯一性。在无摩擦情况下，它是已知的[Schatzman， Nonlinear Anal]。理论，方法，应用2(1978)355-373]，非唯一性的病理可以存在，即使所有的数据都是类C∞。然而，如果数据是解析的，则恢复唯一性[Ballard， Arch。合理的机械。[j].地理学报。2004(5):387 - 398。在此解析性假设下，我们证明了具有单边接触和库仑摩擦的动力问题解的存在唯一性，推广了[Ballard， Arch.]合理的机械。肛。154(2000)199-274]的情况下，库仑摩擦增加到单边接触。
A simple dynamical problem involving unilateral contact and dry friction of Coulomb type is considered as an archetype. We are concerned with the existence and uniqueness of solutions of the system with Cauchy data. In the frictionless case, it is known [Schatzman, Nonlinear Anal. Theory, Methods Appl. 2 (1978) 355–373] that pathologies of non-uniqueness can exist, even if all the data are of class C ∞ . However, uniqueness is recovered provided that the data are analytic [Ballard, Arch. Rational Mech. Anal. 154 (2000) 199–274]. Under this analyticity hypothesis, we prove the existence and uniqueness of solutions for the dynamical problem with unilateral contact and Coulomb friction, extending [Ballard, Arch. Rational Mech. Anal. 154 (2000) 199–274] to the case where Coulomb friction is added to unilateral contact.