|
Abstract:
Chemotaxis models are systems of PDEs arising from mathematical biology where they are used to describe simple organisms that are able to direct their movement according to the concentration gradient of a chemical substance. They play a role in so different contexts as aggregation patterns in bacteria, formation of slime moulds, skin pigmentation patterns, angiogenesis in tumor progression and wound healing.
The most important examples of these systems are the Keller-Segel model and relatives thereof.
Mainly due to the presence of cross-diffusive terms, they pose challenging analytical questions and lead to insights on e.g. structure formation, in its most extreme form signified by blow-up of solutions in finite or infinite time. Over the last decades, they have brought forth an active area of research and a large amount of literature.
This special session will focus on recent analytical results concerned with the qualitative behavior of solutions to these systems, in accordance with current trends possibly including effects of coupling to other processes, like population growth, the interplay with a surrounding fluid, haptotaxis models, or interactions of several chemo-tactically active species. Examples of qualitative properties of interest are the question of boundedness versus blow-up, large-time behavior or the emergence of patterns.
An important goal of this special session is to bring together young researchers and experts working in these areas, in order to stimulate discussion, facilitate the emergence of new ideas, and inspire new research.
|
