Manas Bhatnagar

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.  I was a Visiting Assistant Professor (Postdoc position) in the Department of Mathematics and Statistics at University of Massachusetts Amherst from Sep '22 to Aug '25. Currently, I am an Associate Lecturer at University of Massachusetts Boston.

Curriculum Vitae                     Research Statement                                                   Teaching Statement

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

Publications

1. On critical thresholds for hyperbolic balance law systems,
   with H. Liu,
   Hyperbolic Problems: Theory, Numerics, Applications, 1,145--155, 2024.
   DOI, ArXiv preprint

2. 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

3. 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 

4. 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

5.  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

6. 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

7. 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

1. Weak* Solutions III: A Convergent Front Tracking Scheme,
   with R. Young,
   ArXiv preprint

2. A complete characterization of sharp thresholds to spherically symmetric multidimensional pressureless Euler-Poisson systems,
   with H. Liu.
   ArXiv preprint