Blowup solutions to the Keller-Segel system
I will present the construction of various blowup solutions to the Keller-Segel system, including exact self-similar solutions, those exhibiting asymptotically self-similar profiles, and the formation of single-collapsing blowup. Furthermore, the talk will cover more complex patterns such as multiple-collapsing, standing-ring and collapsing-ring blowup, showcasing the rich phenomenology achievable through these rigorous constructions.