Mathematics Seminar - 10/29/21

Abstract:  We prove the global existence of a unique strong solution to the initial boundary-value problem for a fourth-order exponential PDE modeling crystal surface growth. The model we study is derived as the limit of a microscopic Markov jump process with Metropolis-type transition rates. Our investigation reveals that, in opposition to the models with Arrhenius rates, where the exponent may contain a singular part, the exponent in our model is a $ W^{1,2} $ function.