Abstract
Moreau has shown that a Yosida-type regularization procedure can be used in order to prove the existence of a solution to the so-called sweeping process or evolution problem associated with a moving convex set (see e.g. [Mor 3]). If this set is supposed to be Lipschitz-continuous in the sense of Hausdorff distance, then the solution to the problem it defines is also Lipschitz-continuous with respect to a real variable t. The Yosida or Moreau-Yosida approximants, that is, the absolutely continuous solutions to the regularized differential equations derived from the initial problem, then converge uniformly to the solution to the sweeping process.
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© 1993 Springer Basel AG
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Marques, M.D.P.M. (1993). Regularization and Graph Approximation of a Discontinuous Evolution. In: Differential Inclusions in Nonsmooth Mechanical Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 9. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7614-8_2
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DOI: https://doi.org/10.1007/978-3-0348-7614-8_2
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7616-2
Online ISBN: 978-3-0348-7614-8
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