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Aspects of global solvability in cross-diffusive parabolic systems
Introduction and preamble; some results and an overview
Overview
Introduction and preamble; some results and an overview
Previous publications and their relation to this dissertation
Overview
A closer look at the heat equation and some useful estimates
Blow-up profiles and refined extensibility criteria in some quasilinear Keller-Segel systems
Introduction and main result
Setting parameters
The case kappa>=m+1
The case kappa<m+1
Extending the maximal existence time
Global existence and boundedness in a chemorepulsion system with superlinear diffusion
Introduction and main result
Uniform boundedness of classical solutions for nondegenerate diffusion and the proof of theorem 1
Introduction and existence of weak solutions
The fast signal diffusion limit in nonlinear chemotaxis systems
Introduction and main result
Existence of global classical solutions to the fully parabolic system and some bounds
Solutions of the parabolic-elliptic system
Global solutions to a higher-dimensional system related to crime modelling
Introduction and main result
Local solutions and a criterion for global existence
Initial estimates for u and v
Higher regularity for u and the proof of theorem V.1.1
Energy solutions for eventually vanishing diffusion in a subcritical setting
Introduction and main result
Introduction of very weak energy solutions
Global solutions to the approximating systems
Passing to the limit and proving the main result
Dissertation (PhD)
Aspects of global solvability in cross-diffusive parabolic systems / Rachel Charlotte Freitag
Place and Date of Creation
Paderborn
2021
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