Aspects of global solvability in cross-diffusive parabolic systems / Rachel Charlotte Freitag. Paderborn, 2021
Content
- 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
- 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