Sweeping by a tame process
نویسنده
چکیده
We show that any semi-algebraic sweeping process admits piecewise absolutely continuous solutions, and any such bounded trajectory must have finite length. Analogous results hold more generally for sweeping processes definable in o-minimal structures. This extends previous work on (sub)gradient dynamical systems beyond monotone sweeping sets.
منابع مشابه
Trajectory length of the tame sweeping process
We show that bounded trajectories of the semi-algebraic, or more generally o-minimally definable, sweeping process have finite length. This result generalizes previous work on gradient/subgradient dynamical systems and paves the way for further extensions in control systems and mathematical mechanics.
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