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

Lorenz, Thomas

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 28 (2008) no. 1, pp. 15-73.

Résumé

Similarly to quasidifferential 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. In spite of lacking any linear structures, a distribution-like approach leads to so-called right-hand forward solutions.

Détail

Keywords: mutational equations, quasidifferential equations, funnel equations, nonlocal geometric evolutions, reachable sets of differential inclusions, sets of positive erosion, sets of positive reach

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