TY  - GEN
KW  - Mutationsgleichungen 
KW  -  nichtsymmetrische Abstandsfunktionen 
KW  -  nichtlokale geometrische Evolutionen 
KW  -  erreichbare Mengen von DifferentialinklusionenMutational equations 
KW  -  quasidifferential equations 
KW  -  nonlocal geometric evolutions
KW  -  reachable sets of differential inclusions 
KW  -  sets of positive reach
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/7392/
Y1  - 2007///
ID  - heidok7392
AV  - public
N2  - 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.
TI  - Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms
A1  - Lorenz, Thomas
ER  -