This monograph extends the classical concept of ordinary differential equations in the Euclidean space to nonempty sets which are just supplied with a family of "continuous" distance functions. In particular, these sets are not supposed to have any linear structure or to be metric spaces. The main goal is a joint framework for continuous dynamical systems beyond the traditional border of vector spaces so that examples of completely different origins can be coupled in systems. It is motivated by the mutational equations introduced by Jean-Pierre Aubin in the 1990s. Some of the examples discussed here are: nonlocal set evolutions, semilinear evolution equations, nonlinear transport equations for finite Radon measures, functional stochastic differential equations, parabolic differential equations in noncylindrical domains. This monograph is my revised Habilitationsschrift (i.e. thesis for a postdoctoral lecture qualification in Germany) submitted to the Faculty of Mathematics and Computer Science at Heidelberg University in January 2009.
|Supervisor:||Jäger, Prof. Dr. Willi|
|Date of thesis defense:||1 July 2009|
|Faculties / Institutes:||Service facilities > Interdisciplinary Center for Scientific Computing|
|Controlled Keywords:||Verallgemeinerte Differentialgleichung, Nichtlineare Evolutionsgleichung, Nichtglatte Analysis, Mengenwertige Abbildung|
|Uncontrolled Keywords:||Mutationsgleichungen , nichtsymmetrische Abstandsfunktionen , nichtlokale geometrische Evolutionen , erreichbare Mengen von Differentialinklusionen|