%0 Generic
%A Lorenz, Thomas
%D 2004
%F heidok:4949
%K Mutationsgleichungen , nichtsymmetrische Abstandsfunktionen , nichtlokale geometrische Evolutionen , erreichbare Mengen von Differentialinklusionengeneralized ODE on sets with nonsymmetric distance functions , nonlocal geometric evolutions , mutational equations , set-valued maps
%R 10.11588/heidok.00004949
%T First-order geometric evolutions and semilinear evolution equations : a common mutational approach
%U https://archiv.ub.uni-heidelberg.de/volltextserver/4949/
%X 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).