First-order geometric evolutions and semilinear evolution equations : a common mutational approach

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).

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Heidelberg

Year

2004

Author dc:creator

• Lorenz, Thomas

Contributors dc:contributor

• Jäger, Willi

Repository record source_url

http://www.ub.uni-heidelberg.de/archiv/4949

OAI identifier oai:identifier

oai:archiv.ub.uni-heidelberg.de:4949