Random moving domain
Ana Djurdjevac · arXiv (Cornell University) · 2018
We analyse the well-posedness of the heat equation on a random time-dependent flat domain. We investigate the necessary conditions for the random velocity filed that will induce required regularity of the associated vector flow. We define the appropriate setting for considering the heat equation on a random non-cylindrical domain. Furthermore, we apply the domain mapping method and derive the associated partial differential equation on a fixed domain with a particular random coefficient. Under suitable assumptions, we prove the existence and uniqueness of the later equation.