14 citations · 24 across the 12 of their papers we have counts for
17 papers
Lower Bounds for Advection-Diffusion Equations: An Exploration with AI-Generated Proofs
Chenyang An, Xiaoqian Xu
We establish explicit lower bounds for advection-diffusion equations in three settings: a polynomial bound for inviscid shears with , a uni…
Accelerating sampling via asymptotic relaxation enhancing flows
Yuanyuan Feng, Lei Li, Jian-Guo Liu +1
In this paper, we accelerate Langevin Monte Carlo sampling from Gibbs measures by adding a large drift that preserves the invariant measure. For warm-start init…
Data-Driven Parameter Identification for Tumor Growth Models
Liu Liu, Yifei Wang, Qinyu Xu +1
Modeling tumor growth accurately is essential for understanding cancer progression and informing treatment strategies. To estimate the parameters in the tumor growth model describe…
Sequential Exponential Lower Bounds for the Advection-Diffusion Equation with Shear Flows
Yupei Huang, Xiaoqian Xu
In this paper, we prove that the norm of spatial mean-free solutions to the advection--diffusion equation on with shear drifts satisfies an \emph{exponential l…
Phase separation for the 2D Cahn-Hilliard equation with a background shear flow
Yu Feng, Yuanyuan Feng, Anna L. Mazzucato +1
We consider the Cahn-Hilliard equation, which models phase separation in binary fluids, on the two-dimen\-sional torus in the presence of advection by a given background shear flow…
A Three-dimensional tumor growth model and its boundary instability
Jian-Guo Liu, Thomas Witelski, Xiaoqian Xu +1
In this paper, we investigate the tumor instability by employing both analytical and numerical techniques to validate previous results and extend the analytical findings presented…