Young Researchers Workshop:
Multiscale phenomena: modeling, analysis and computation

Coalescing diffusion in the Keller-Segel model

Gleb Zhelezov

University of Arizona

It is known that the Keller-Segel model for chemotaxis can exhibit the formation of singularities in finite time, past which the system cannot be propagated. We will introduce a stochastic particle regularization of this system, in which the formation of singularities corresponds to the coalescence of particle aggregates into several massive particles of low variance. We will discuss some of the analytical and statistical properties of this particle system, and present a (particle-based) numerical method for solving the K-S system in the plane.