TY  - GEN
A1  - Lorenz, Thomas
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/5519/
N2  - The primary aim is to unify the definition of  solution  for completely different types of evolutions. Such a common approach is to lay the foundations for solving systems like, for example, a semilinear evolution equation (of parabolic type) in combination with a first order geometric evolution. In regard to geometric evolutions, this concept is to fulfill 3 conditions : First, consider nonempty compact subsets K(t) of R^N without a priori restrictions on the regularity of the boundary. Second, the evolution of K(t) might depend on nonlocal properties of the set K(t) and its normal cones. Last, but not least, no inclusion principle.  The approach here is based on generalizing the mutational equations of Aubin for metric spaces in two respects : Replacing the metric by a countable family of (possibly nonsymmetric) distances (called ostensible metrics) and extending the basic idea of distributions.
TI  - Evolution equations in ostensible metric spaces : Definitions and existence.
ID  - heidok5519
AV  - public
KW  - Mutationsgleichungen 
KW  -  nichtsymmetrische Abstandsfunktionen 
KW  -  nichtlokale geometrische Evolutionen 
KW  -  erreichbare Mengen von Differentialinklusionengeneralized ODE on sets with nonsymmetric distance functions 
KW  -  nonlocal geometric evolutions 
KW  -  mutational equations 
KW  -  set-valued maps
Y1  - 2005///
T3  - IWR-Preprints
ER  -