TY  - GEN
A1  - Lorenz, Thomas
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/4949/
N2  - The primary aim of this Ph.D. thesis 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 whose components have their origins in  diverse applications. The analytical touchstone of the general character consists of (1.) a semilinear evolution equation in a reflexive Banach space and (2.) a first-order geometric evolution, i.e. a time-dependent compact subset of R^n, whose deformation depends on nonlocal properties of normal cones at the boundary. (No inclusion principle is assumed.)    Taking up the widespread idea of derivatives as first-order approximations, distance functions (maybe in a generalized sense) are required and essentially the only tool to use for a general approach beyond vector spaces.  Here two concepts are presented, both of which are based on generalizing the mutational equations of Jean-Pierre Aubin (in metric spaces) to a set with a countable family of so-called ostensible metrics (that need not be symmetric).
AV  - public
TI  - First-order geometric evolutions and semilinear evolution equations : a common mutational approach
Y1  - 2004///
ID  - heidok4949
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
ER  -