In this note, we prove the existence of solutions for the sweeping process problem x$(t) # &N C(t) (x(t)) a.e., x(t) # C(t), x(0)=x 0 # C(0), where C(.) is an arbitrary Hausdorff Lipschitzean multifunction, from I=[0, T] onto the set of nonempty closed subsets of R d . This generalizes a well known
โฆ LIBER โฆ
Regularization of Nonconvex Sweeping Process in Hilbert Space
โ Scribed by Thibault, Lionel
- Publisher
- Springer
- Year
- 2008
- Tongue
- English
- Weight
- 373 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0927-6947
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We consider a nonlinear differential stochastical equation in a Hilbert space, that is, a Lipschitzian perturbation of a linear equation. We prove that, under suitable hypotheses, both equations have invariant measures \(\mu\) and \(\mu_{0}\) respectively and that \(\mu\) is absolutely continuous wi