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Evolution equations in ostensible metric spaces. II. Examples in Banach spaces and of free boundaries.

Lorenz, Thomas

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Abstract

In part I, generalizing mutational equations of Aubin in metric spaces has led to so-called right-hand forward solutions in a nonempty set with a countable family of (possibly nonsymmetric) ostensible metrics. Now this concept is applied to two different types of evolutions that have motivated the definitions : semilinear evolution equations (of parabolic type) in a reflexive Banach space and compact subsets of R^N whose evolution depend on nonlocal properties of both the set and their limiting normal cones at the boundary. For verifying that reachable sets of differential inclusions are appropriate transitions for first-order geometric evolutions, their regularity at the boundary is studied in the appendix.

Item Type: Preprint
Series Name: IWR-Preprints
Date Deposited: 18 May 2005 13:55
Date: 2005
Faculties / Institutes: Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 510 Mathematics
Controlled Keywords: Verallgemeinerte Differentialgleichung, Nichtlineare Evolutionsgleichung, Nichtglatte Analysis, Mengenwertige Abbildung, Stark stetige Halbgruppe
Uncontrolled Keywords: Mutationsgleichungen , nichtsymmetrische Abstandsfunktionen , nichtlokale geometrische Evolutionen , erreichbare Mengen von Differentialinklusionengeneralized ODE on sets with nonsymmetric distance functions , nonlocal geometric evolutions , mutational equations , set-valued maps
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