ISSN:
1572-932X
Keywords:
measure differential inclusions
;
hemicontinuous
;
weak* closure
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Measure differential inclusions were introduced by J. J. Moreau to study sweeping processes, and have since been used to study rigid body dynamics and impulsive control problems. The basic formulation of an MDI is “d μ / d ν(t) ∈ K(t)” where μ is a vector measure, ν an unsigned measure, and K(⋅) is a set-valued map with closed, convex values and is hemicontinuous. Note that μ need not be absolutely continuous with respect to ν. Stewart extended Moreau's original concept (which applied only to cone-valued K(⋅)) to general convex sets, and gave strong and weak formulations of “d μ / d ν(t) ∈ K(t)” where K(t) ⊂ R n . Here the strong and weak formulations of Stewart are extended to infinite-dimensional problems where K(t) ⊂ X where X is a separable reflexive Banach space; they are shown to be equivalent under mild assumptions on K(⋅).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008789529348
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