Numerical aspects of the sweeping process
نویسندگان
چکیده
منابع مشابه
Convergence Order of a Numerical Scheme for Sweeping Process
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2 Mathematical framework and well-posedness results 4 2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Uniform prox-regularity of sets Q(t) . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Lipschitz regularity of Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Well-posedness results . . . . . . . . . . . . . . . ....
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In this paper we present an extension of Moreau’s sweeping process for higher order systems. The dynamical framework is carefully introduced, qualitative, dissipativity, stability, existence, regularity and uniqueness results are given. The time-discretization of these nonsmooth systems with a timestepping algorithm is also presented. This differential inclusion can be seen as a mathematical fo...
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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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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.
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ژورنال
عنوان ژورنال: Computer Methods in Applied Mechanics and Engineering
سال: 1999
ISSN: 0045-7825
DOI: 10.1016/s0045-7825(98)00387-9