Jian-Guo Liu
Duke University
351 Papers
1.2K Citations
Jian-Guo Liu is an academic researcher from Duke University. The author has contributed to research in topics: Nonlinear system & Boundary value problem. The author has an hindex of 45, co-authored 327 publications. Previous affiliations of Jian-Guo Liu include Virginia Tech & Temple University.
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Papers
•Posted Content
Mathematical validation of the Peierls--Nabarro model for edge dislocations
TL;DR: In this article, the Peierls-Nabarro (PN) model is validated in terms of both governing equations and energy variations, and it is shown that a static solution is a global minimizer in perturbed sense.
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Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamics
TL;DR: In this article, the authors study the tumor growth equation along with various models for the nutrient component, including the \emph{in vitro} model and the ǫ-in vivo model, and derive several analytical solutions to the Hele-Shaw flow models.
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Meanfield games and model predictive control
TL;DR: In this paper, the authors explore the link between Mean-Field games and the best-reply strategy approach and propose a Model Predictive Control framework, which consists of setting the mean-field game over a short time interval which recedes as time moves on.
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Convergence of Diffusion-Drift Many Particle Systems in Probability Under a Sobolev Norm
Jian-Guo Liu,Yuan Zhang +1 more
- 01 Jan 2016
TL;DR: In this paper, a martingale method was developed to show the convergence of the regularized empirical measure of many particle systems in probability under a Sobolev norm to the corresponding mean field PDE.
Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects
TL;DR: Weare et al. as discussed by the authors presented a non-rigorous derivation of the full model derived with a quadratic interaction potential using the rates and methods of the last author with Jonathan Weare (PRE, 2013).