Speaker: Dr. Le Chen (Auburn)

Title: Superlinear stochastic heat equation

Abstract: In this talk, we will discuss the superlinear stochastic heat equation. It is known that when the forcing term and the diffusion coefficient are Lipschitz continuous, there exists a unique random field solution for all time, which is called global solution. We explore the existence of a global solution when the Lipschitz condition are replaced by certain superlinear growth conditions. This gives another instance of the delicate balance between the smoothing effect of the heat kernel and the roughening effect of the multiplicative noise.

 

This talk will be based on a recent work with Jingyu Huang and an ongoing project with Mohammud Foondun, Jingyu Huang, and Mickey Salins.