Publications [#335607] of Jian-Guo Liu

Papers Published

1. Gao, Y; Liu, JG; Lu, XY; Xu, X, Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface, Calculus of Variations and Partial Differential Equations, vol. 57 no. 2 (April, 2018), Springer Nature [doi]
   (last updated on 2024/04/19)

   Abstract:
   In this work we consider (Formula presented.) which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the problem as the gradient flow of a suitably-defined convex functional in a non-reflexive space. Then by restricting it to a Hilbert space and proving the uniqueness of its sub-differential, we can apply the classical maximal monotone operator theory. The mathematical difficulty is due to the fact that whh can appear as a positive Radon measure. We prove the existence of a global strong solution with hidden singularity. In particular, (1) holds almost everywhere when whh is replaced by its absolutely continuous part.