132 citations · 914 across the 68 of their papers we have counts for
68 papers
On critical thresholds for hyperbolic balance law systems
Manas Bhatnagar, Hailiang Liu
We review the theoretical development in the study of critical thresholds for hyperbolic balance laws. The emphasis is on two classes of systems: Euler-Poisson-alignment (EPA) syst…
A complete characterization of sharp thresholds to spherically symmetric multidimensional pressureless Euler-Poisson systems
Manas Bhatnagar, Hailiang Liu
The Euler-Poisson (EP) system models the dynamics of a variety of physical processes, including charge transport, collisional plasmas, and certain cosmological wave phenomena. In t…
Anderson acceleration of gradient methods with energy for optimization problems
Hailiang Liu, Jia-Hao He, Xuping Tian
Anderson acceleration (AA) as an efficient technique for speeding up the convergence of fixed-point iterations may be designed for accelerating an optimization method. We propose a…
On the invariant region for compressible Euler equations with a general equation of state
Hailiang Liu, Ferdinand Thein
The state space for solutions of the compressible Euler equations with a general equation of state is examined. An arbitrary equation of state is allowed, subject only to the physi…
Global Dynamics and Photon Loss in the Kompaneets Equation
Joshua Ballew, Gautam Iyer, C. David Levermore +2
The Kompaneets equation governs dynamics of the photon energy spectrum in certain high temperature (or low density) plasmas. We prove several results concerning the long-time conve…
SGEM: stochastic gradient with energy and momentum
Hailiang Liu, Xuping Tian
In this paper, we propose SGEM, Stochastic Gradient with Energy and Momentum, to solve a large class of general non-convex stochastic optimization problems, based on the AEGD metho…