EXISTENCE OF DENDRITIC CRYSTAL-GROWTH WITH STOCHASTIC PERTURBATIONS

We prove the first mathematical existence result for a model of dendri tic crystal growth with thermal fluctuations. The incorporation of noi se is widely believed to be important in solidification processes. Our result produces an evolving crystal shape and a temperature field sat isfying the Gibbs-Thomson condition at the crystal interface and a hea t equation with a driving force in the form of a spatially correlated white noise. We work in the regime of infinite mobility, using a sharp interface model with a smooth and elliptic anisotropic surface energy . Our approach permits the crystal to undergo topological changes. A t ime discretization scheme is used to approximate the evolution. We com bine techniques from geometric measure theory and stochastic calculus to handle the singular geometries and take advantage of the cancellati on properties of the white noise.