Special Session 115: Mathematical Models of Chemotaxis

Chemotaxis is the ability of living organisms to orientate their movement towards or away a chemical substance. The term was introduced to describe cell migration observed during the early days of the development of microscopy in the XIX century. As the technology advanced, chemotactic mechanisms have turned out to be of outstanding relevance in numerous biological processes such as immune system response, embryonic development, tumor growth, or bacterial cluster formation, for instance. In the past decades, after the pionering works of Keller and Segel in the 1970s, various chemotaxis processes have been described mathematically by using systems of evolutionary PDEs with nonlinear cross-diffusive terms as their most characteristic ingredient. Particular mathematical challenges originate from the fact that this chemotactic cross-diffusion can enforce singularity formation of solutions, thus letting even the basic questions of existence theory become nontrivial in many situations. Although such explosions have been detected in certain rather special chemotaxis systems under appropriate assumptions, a comprehensive understanding of these selforganizing features is still lacking. Accordingly, the analysis of chemotaxis systems still forms a very active field of mathematical research, involving steadily increasing expertise from various fields in PDE analysis. The proposed special session intends to showcase recent trends in the mathematics of chemotaxis systems. A particular focus will be on topics and techniques related to rigorous mathematical analysis, but also novel aspects in modeling and simulation will be addressed. We thereby aim at bringing together experts from different branches in the mathematics of chemotaxis, ranging from essentially mathematically motivated to mainly application-oriented, but also ranging from experienced specialists to auspicious young researchers, in order to provide rich opportunities for fruitful and multilateral discussion.