36 citations · 69 across the 28 of their papers we have counts for
5 papers · 1 filter
Existence theorems for a crystal surface model involving the p-Laplace operator
Xiangsheng Xu
The manufacturing of crystal films lies at the heart of modern nanotechnology. How to accurately predict the motion of a crystal surface is of fundamental importance. Many continuu…
Logarithmic upper bounds for weak solutions to a class of parabolic equations
Xiangsheng Xu
It is well known that a weak solution to the initial boundary value problem for the uniformly parabolic equation $\partial_tφ-\mbox{div}(A\nabla φ) +ωφ= f $ in $Ω_T\equivΩ\time…
Partial regularity of weak solutions and life-span of smooth solutions to a biological network formulation model
Xiangsheng Xu
In this paper we first study partial regularity of weak solutions to the initial boundary value problem for the system $-\mbox{div}\left[(I+\mathbf{m}\otimes \mathbf{m})\nabla p\ri…
Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface
Yuan Gao, Jian-Guo Liu, Xin Yang Lu +1
In this work we consider which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the pr…
Local and global existence of solutions to a fourth-order parabolic equation modeling kinetic roughening and coarsening in thin films
Xiangsheng Xu
In this paper we study both the Cauchy problem and the initial boundary value problem for the equation $\partial_tu+\mbox{div}\left(\nablaΔu-{\bf g}(\nabla u)\right)=0$. This equat…