On Liouville systems, Moser Trudinger inequality and Keller-Segel equations of chemotaxis

PDE Seminar
Tuesday, March 24, 2020 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 006
Gershon Wolansky – Israel Institute of Technology – gershonw@math.technion.ac.ilhttp://www2.math.technion.ac.il/~gershonw/
Albert Fathi
The Liouville equation is a semi-linear elliptic equation of exponential non-linearity. Its non-local version is a steady state of the Keller-Segel equation representing the distribution of living cells, such as slime molds. I will represent an extension of this equation to multi-agent systems and discuss some associated critical phenomena, and recent results with Debabrata Karmakar on the parabolic Keller segel system and its asymptotics in both critical and non-critical cases.