A functional inequality and its applications to a class of nonlinear fourth-order parabolic equations

Abstract

In this article we study the initial-boundary value problem for a family of nonlinear fourth order parabolic equations. The classical quantum drift-diffusion model is a member of the family. Two new existence theorems are established. Our approach is based upon a semi-discretization scheme, which generates a sequence of positive approximate solutions, and a functional inequality of the type