Uniqueness and continuous dependence on data for one-dimensional impact problems
Résumé
One dimensional dynamics with impact are described by the data of a closed interval $K$, a function $f$ of time, position, and velocity, and a restitution coefficient $e \in [0,1)$. When $u$ is in the interior of $K$, it satisfies the ordinary differential equation $\ddot{u} =f(t,u,\dot{u})$. When it hits the end points of $K$, the velocity is reversed and multiplied by $e$. If f is analytic with respect to its three arguments, it is proved that uniqueness holds for the forward Cauchy problem.
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