10 citations · 14 across the 9 of their papers we have counts for
9 papers
A Convergent Front Tracking Scheme
Manas Bhatnagar, Robin Young
We present a modified Front Tracking (mFT) scheme for hyperbolic systems of conservation laws in one space dimension, in which we allow arbitrarily large nonlinear waves. We build…
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…
Critical thresholds in the Euler-Poisson-alignment system
Manas Bhatnagar, Hailiang Liu, Changhui Tan
This paper is concerned with the global wellposedness of the Euler-Poisson-alignment (EPA) system. This system arises from collective dynamics, and features two types of nonlocal i…
Global dynamics of the Euler-alignment system with weakly singular kernel
Manas Bhatnagar, Hailiang Liu
This letter studies the Euler-alignment system with weakly singular influence functions by introducing a novel technique to bound the density. Instead of resorting to a nonlinear m…
Sharp critical thresholds in a hyperbolic system with relaxation
Manas Bhatnagar, Hailiang Liu
We propose and study a one-dimensional hyperbolic Eulerian system with local relaxation from critical threshold phenomena perspective. The system features dynamic trans…
Critical thresholds in a nonlocal Euler system with relaxation
Manas Bhatnagar, Hailiang Liu
We propose and study a nonlocal Euler system with relaxation, which tends to a strictly hyperbolic system under the hyperbolic scaling limit. An independent proof of the local exis…
Critical thresholds in 1D pressureless Euler-Poisson systems with varying background
Manas Bhatnagar, Hailiang Liu
The Euler Poisson equations describe important physical phenomena in many applications such as semiconductor modeling and plasma physics. This paper is to advance our understanding…
Critical Thresholds in One Dimensional Damped Euler-Poisson Systems
Manas Bhatnagar, Hailiang Liu
This paper is concerned with the critical threshold phenomenon for one dimensional damped, pressureless Euler-Poisson equations with electric force induced by a constant background…