SS13 AIMS 2016 Meeting, Orlando, Florida, USA

Title:  Chemotactic cross-diffusion in complex frameworks
Organizer(s):
Name: Affiliation: Country: Email Address:
Michael Winkler
U of Paderborn
Germany
michael.winkler@math.upb.de
Dariusz Wrzosek
U of Warsaw
Poland
dwrzosek99@gmail.com
Introduction:
Chemotaxis is a ubiquitously observed mechanism of interaction between individuals (cells or organisms) in biological systems. Typically the chemotactic interaction is mediated be a chemical agent whose density gradient determines the direction of movement of the individuals. Chemotaxis mechanisms are known to play outstanding roles in numerous processes of self organization at all levels of complexity of biological systems. According to various modeling approaches, an adequate mathematical description thereof requires the study of parabolic PDE systems involving certain cross-diffusive terms as their most characteristic ingredient. Important results in the literature identify situations in which in the framework of basic models, such chemotactic cross-diffusion indeed enforces spontaneous generation of structures or space-time patterns e.g. in the sense of stabilization toward non-constant equilibria, or even in the sense of singularity formation. The goal of the proposed special session is to present up-to-date results in the analysis of chemotaxis systems, with emphasis on qualitative properties of solutions such as boundedness and asymptotic behavior or the occurrence of blow-up or pattern formation. According to recent developments in both modeling and analysis, a particular focus will be on models for chemotactic cross-diffusion in complex frameworks, including couplings to further mechanisms such as cell proliferation, haptotaxis, or also interaction with a surrounding fluid. By planning to bring together experienced and young researchers working in these areas, we intend to stimulate a fruitful sharing of ideas, and thereby to initiate new directions of future research.
List of approved abstract