Manas Bhatnagar

Visiting Assistant Professor, Department of Mathematics and Statistics

LGRT 1634, University of Massachusetts Amherst, 01003

Email: mbhatnagar[at]umass[dot]edu

University of Massachusetts Amherst (Directory)

Hyperbolic Balance Laws are the equations that intrigue me the most. My fields of interest fall under the wider area of Analysis of Partial Differential Equations. I graduated in Summer 2022 with a PhD in Mathematics from Iowa State University. Currently, I am a Visiting Assistant Professor (Postdoc position) in the Department of Mathematics and Statistics at University of Massachusetts Amherst.

Curriculum Vitae Research Statement Teaching Statement

Postdoc Mentor: Dr Robin Young
Ph.D. Advisor: Dr Hailiang Liu

Publications

On critical thresholds for hyperbolic balance law systems,
with H. Liu,
Hyperbolic Problems: Theory, Numerics, Applications, 1,145--155, 2024.
DOI, ArXiv preprint
Critical Thresholds in the Euler-Poisson-alignment system,
with H. Liu and C. Tan,
Journal of Differential Equations, 375, 82--119, 2023.
DOI, ArXiv preprint
Global dynamics of the one-dimensional Euler-alignment system with weakly singular kernel,
with H. Liu,
Applied Mathematics Letters, 128, 107856, 2022.
DOI, ArXiv preprint
Sharp critical thresholds in a hyperbolic system with relaxation,
with H. Liu,
Discrete and Continuous Dynamical Systems, 41(12), 5851--5869, 2021.
DOI, ArXiv preprint, Talk Slides, Poster
Well-posedness and critical thresholds in a nonlocal Euler system with relaxation,
with H. Liu,
Discrete and Continuous Dynamical Systems, 41(11): 5271--5289, 2021.
Online version available:
DOI, ArXiv preprint, Talk Slides, Poster
Critical thresholds in 1D pressureless Euler-Poisson systems with variable background,
with H. Liu,
Physica D: Nonlinear Phenomena, 414, 132728, 2020.
DOI, ArXiv, Talk Slides
Critical thresholds in one dimensional damped Euler-Poisson systems,
with H. Liu,
Mathematical Models and Methods in Applied Sciences, 30(05), 891--916, 2020.
DOI, ArXiv, Poster

Preprints

Weak* Solutions III: A Convergent Front Tracking Scheme,
with R. Young,
ArXiv preprint
A complete characterization of sharp thresholds to spherically symmetric multidimensional pressureless Euler-Poisson systems,
with H. Liu.
ArXiv preprint