Minisymposium: Nonlinear Diffusion Processes: Cross Diffusion, Complex Diffusion and Related Topics
Nonlinear diffusion equations have attracted a lot of attention over the last few years in many practical applications. After the pioneering work of Keler and Segel in the 1970s, cross-diffusion models became very popular in biology, chemistry and physics to emulate systems with multiple species. The range of application is even wider and, in particular, complex-diffusion models are of special relevance for example in the field of image processing. Meanwhile the underlying mathematical theory has been developed in a synergetic way with applications, in recent years, this topic became the focus of an intensive research within the mathematics community. In spite of the relevance of cross-diffusion models in numerous fields of application and all the mathematical activity around them, important questions remain unanswered and meaningful challenging problems still need to be addressed.