36 citations · 69 across the 28 of their papers we have counts for
4 papers · 1 filter
Regularity theorems for a biological network formulation model in two space dimensions
Xiangsheng Xu
We present several regularity results for a biological network formulation model originally introduced by D. Cai and D. Hu in {\it Phys. Rev. Lett.}, {\bf 111}(2013), 138701. A con…
Partial regularity of weak solutions to a PDE system with cubic nonlinearity
Jian-Guo Liu, Xiangsheng Xu
In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly si…
Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions
Jian-Guo Liu, Xiangsheng Xu
In this paper we are concerned with the existence of a weak solution to the initial boundary value problem for the equation .…
A Class of Functional Inequalities and their Applications to Fourth-Order Nonlinear Parabolic Equations
Jian-Guo Liu, Xiangsheng Xu
We study a class of fourth order nonlinear parabolic equations which include the thin-film equation and the quantum drift-diffusion model as special cases. We investigate these equ…