Advection-diffusion equations with random coefficients on evolving hypersurfaces

Abstract

We present the analysis of advection-diffusion equations with random coefficients on moving hypersurfaces. We define a weak and a strong material derivative, which account for the spatial movement. Then we define the solution space for these kind of equations, which is the Bochner-type space of random functions defined on a moving domain. We consider both cases, uniform and log-normal distributions of the diffusion coefficient. Under suitable regularity assumptions we prove the existence and uniqueness of weak solutions of the equation under analysis, and also we give some regularity results about the solution.