RT info:eu-repo/semantics/doctoralThesis
T1 Topologies of continuity for Carathéodory differential equations with applications in non-autonomous dynamics
A1 Longo, Iacopo Paolo
A2 Universidad de Valladolid. Escuela de Ingenierías Industriales
K1 Ecuaciones diferenciales
K1 Ecuaciones Funcionales
K1 12 Matemáticas
AB The theory developed in this work allows to extend the skew-product formalism to Carathéodory ordinary differential equations and delay differential equations with constant delay through the use of strong and weak metric topologies of integral type. As a result, one obtains a variety of tools from topological dynamics to study the qualitative behavior of the solutions of such classes of differential problems. As an example, the work includes several applications for Carathéodory ODEs such as linearized skew-product flows, propagation of the exponential dichotomy and of the dichotomy spectrum of a linear system and study of pullback and global attractors, as well as some simple motivational examples taken from modelizations of real phenomena, which aim to show the applicability of the theory. Additionally, the thesis provides a rich description of the topological structure ofthe considered spaces of Carathéodory functions (among which, some are new) presenting, for example, characterizations of the classes of equivalences for functions which differ on negligible subset of the domain, propagation of properties on the so-called m-bounds and l-bounds through the limits in the given topologies, andsuffcient conditions of relative compactness for subsets of Lipschitz Carathéodory functions.
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/44162
UL http://uvadoc.uva.es/handle/10324/44162
LA eng
NO Departamento de Matemática Aplicada
DS UVaDOC
RD 27-nov-2024