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primary topic: Generalizing evolution equations in ostensible metric spaces: Timed right-hand sleek solutions provide uniqueness of first-order geometric examples.

Generalizing evolution equations in ostensible metric spaces: Timed right-hand sleek solutions provide uniqueness of first-order geometric examples.
type: Article
abstract: The mutational equations of Aubin extend ordinary differential equations to metric spaces (with compact balls). In first-order geometric evolutions, however, the topological boundary need not be continuous in the sense of Painleve–Kuratowski. So this paper suggests a generalization of Aubin’s mutational equations that extends classical notions of dynamical systems and functional analysis beyond the traditional border of vector spaces: Distribution– like solutions are introduced in a set just supplied with a countable family of (possibly non-symmetric) distance functions. Moreover their existence is proved by means of Euler approximations and a form of “weak” sequential compactness (although no continuous linear forms are available beyond topological vector spaces). This general framework is applied to a first-order geometric example, i.e. compact subsets of the Euclidean space evolving according to the nonlocal properties of both the current set and its proximal normal cones. Here neither regularity assumptions about the boundaries nor the inclusion principle are required. In particular, we specify sufficient conditions for the uniqueness of these solutions.
date: 2005
status: published
author list: authors
type: EPrint
type: PreprintEPrint
is part of: repository
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subject: 510 Mathematik

Generalizing evolution equations in ostensible metric spaces: Timed right-hand sleek solutions provide uniqueness of first-order geometric examples. (PDF)
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Generalizing evolution equations in ostensible metric spaces: Timed right-hand sleek solutions provide uniqueness of first-order geometric examples. (PDF)
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Thomas Lorenz
type: Person
given name: Thomas
family name: Lorenz

Generalizing evolution equations in ostensible metric spaces: Timed right-hand sleek solutions provide uniqueness of first-order geometric examples. (Other)
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Generalizing evolution equations in ostensible metric spaces: Timed right-hand sleek solutions provide uniqueness of first-order geometric examples. (Other)
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Generalizing evolution equations in ostensible metric spaces: Timed right-hand sleek solutions provide uniqueness of first-order geometric examples. (Other)
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Generalizing evolution equations in ostensible metric spaces: Timed right-hand sleek solutions provide uniqueness of first-order geometric examples. (Other)
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Generalizing evolution equations in ostensible metric spaces: Timed right-hand sleek solutions provide uniqueness of first-order geometric examples. (Other)
type: Document
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primary topic: Generalizing evolution equations in ostensible metric spaces: Timed right-hand sleek solutions provide uniqueness of first-order geometric examples.

510 Mathematik
type: Concept
preferred label: 510 Mathematics @en