Noise-induced phenomena in stochastic heat equations

 

Stochastic heat equations (SHE) usually refer to heat equations perturbed by noise and can be a model for the density of diffusing particles under a random potential. When the irregularity of noise is dominating the diffusion, SHE exhibits interesting phenomena induced by noise, such as intermittency and dissipation. In this talk, we first introduce what noise means mathematically and present several ways to understand noise-induced phenomena such as intermittency and dissipation.