209 citations · 1.4k across the 114 of their papers we have counts for
7 papers · 2 filters
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…
Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime
Yuan Gao, Jian-Guo Liu, Jianfeng Lu
We study in this work a continuum model derived from 1D attachment-detachment-limited (ADL) type step flow on vicinal surface, , where , considered as a f…
Continuum dynamics of the intention field under weakly cohesive social interactions
Pierre Degond, Jian-Guo Liu, Sara Merino-Aceituno +1
We investigate the long-time dynamics of an opinion formation model inspired by a work by Borghesi, Bouchaud and Jensen. Firstly, we derive a Fokker-Planck type equation under the…
Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces
Yuan Gao, Jian-Guo Liu, Jianfeng Lu
This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton-Cabrera-Frank (BCF) type model following the work [Xiang, SIAM J. A…
Least action principles for incompressible flows and geodesics between shapes
Jian-Guo Liu, Robert L. Pego, Dejan Slepčev
As V. I. Arnold observed in the 1960s, the Euler equations of incompressible fluid flow correspond formally to geodesic equations in a group of volume-preserving diffeomorphisms. W…