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Continuous dependence on data for vibro-impact problems. (English) Zbl 1079.34006
A general vibro-impact problem consists of a mechanical system with a finite number of degrees of freedom subjected to (frictionless) unilateral constraints, acting like “walls”. From the mathematical point of view, if the system is described by a second order ODE, the introduction of unilateral constraints is equivalent to the addition of an adequate measure in the equation plus an impact law of Newton’s type. The author analyzes the continuous dependence of solutions on initial data under an adequate geometrical assumption on the constraints. This study is of interest for the implementation of numerical schemes and computation of approximate solutions (see, the author [J. Differ. Equations 211, No.2, 247-281 (2005; Zbl 1078.34004)]).

MSC:
34A60 Ordinary differential inclusions
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
70F25 Nonholonomic systems related to the dynamics of a system of particles
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