SPEAKER: Eugenia Franco

TITLE: Self-similar solutions to coagulation equations with a source 

ABSTRACT:
The asymptotic behaviour of the solution of the coagulation equation with source, modelling tool in atmospheric science, is not known for the majority of the coagulation kernels. 
In this talk I will sketch a proof of the existence of a self-similar solution for the coagulation equation with source, for a class of homogeneous non-gelling kernels satisfying some upper and lower polynomial bounds.
The self-similar ansatz is supported via matched asymptotics expansions and numerical simulations by S. C. Davies, J. R. King, and J.A.D. Wattis  in their 1999 paper. 
I will end the talk by explaining why proving that the coagulation equation with source at the origin has a unique solution is a fundamental step toward the proof of the self-similar ansatz.