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Motion with a finite number of degrees of freedom with one-sided constraints: The case with loss of energy. (Mouvement à un nombre fini de degrés de liberté avec contraintes unilatérales: Cas avec perte d’énergie.) (French) Zbl 0792.34012
Let \(K\) be a closed convex subset of \(\mathbb{R}^ n\) with a nonempty interior and sufficiently smooth boundary \(\partial K\). Let \(f:[0,T] \times \mathbb{R}^ n \times \mathbb{R}^ n \to \mathbb{R}^ n\) be continuous and Lipschitzian with respect to the last two variables. The authors establish the existence of solutions to the problem \(\ddot u(t)+\partial \psi_ K(u) \ni f(t,u,\dot u)\), \(0 \leq t \leq T\), \(\dot u(t+0)=-e \dot u_ N(t-0)+\dot u_ T(t-0)\), for all \(t\) such that \(u(t) \in \partial K\). Here \(\psi_ K\) is the indicator function of \(K\), \(\partial \psi_ K\) stands for the subdifferential of \(\psi_ K\), \(e \in(0,1]\), and \(\dot u_ N\) (resp. \(\dot u_ T)\) denotes the normal (resp., tangential) component of \(\dot u\).

MSC:
34A60 Ordinary differential inclusions
47J05 Equations involving nonlinear operators (general)
70F25 Nonholonomic systems related to the dynamics of a system of particles
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