Speaker
Luca Ziviani
Description
Run and tumble equations are widely used models for bacterial chemotaxis. In this talk, we present the long-time behavior of run and tumble equations with unbounded velocities. We show existence, uniqueness and quantitative convergence towards a steady state. In contrast to the bounded velocity case, the equilibrium has sub-exponential tails and we have sub-exponential rate of convergence to equilibrium. This produces additional technical challenges. We are able to successfully adapt both Harris' type and L²-hypocoercivity. This is joint work with Emeric Bouin and Josephine Evans.