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Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms

Lorenz, Thomas

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Abstract

Similarly to funnel equations of Panasyuk, the so-called mutational equations of Aubin provide a generalization of ordinary differential equations to locally compact metric spaces. Here we present their extension to a nonempty set with a possibly nonsymmetric distance. A distribution-like approach leads to so-called right-hand forward solutions. This concept is applied to a type of geometric evolution having motivated the definitions : compact subsets of the Euclidean space evolve according to nonlocal properties of both the set and their limiting normal cones at the boundary. The existence of a solution is based on Euler method using reachable sets of differential inclusions as "elementary deformations" (called forward transitions). Thus, the regularity of these reachable sets at the topological boundaries is studied extensively in the appendix.

Item Type: Preprint
Date Deposited: 05 Jun 2007 14:46
Date: 2007
Faculties / Institutes: Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 510 Mathematics
Controlled Keywords: Verallgemeinerte Differentialgleichung, Nichtlineare Evolutionsgleichung, Nichtglatte Analysis, Mengenwertige Abbildung
Uncontrolled Keywords: Mutationsgleichungen , nichtsymmetrische Abstandsfunktionen , nichtlokale geometrische Evolutionen , erreichbare Mengen von DifferentialinklusionenMutational equations , quasidifferential equations , nonlocal geometric evolutions, reachable sets of differential inclusions , sets of positive reach
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