Asymptotic behaviors of global weak solutions for an epitaxial thin film growth equation

Abstract

This paper is concerned with the Dirichlet initial boundary value problem of an epitaxial thin film growth equation involving gradient-type logarithmic nonlinearity and absorption terms. By introducing an equivalent norm and approximating Lipschitz functions, combining with the technique of Faedo–Galerkin approximation and the family of potential wells, we establish the well-posedness of global weak solutions. Meantime, we classify the decay properties and grow-up phenomenon of the considered problem by using the energy functional and the related Nehari manifold.