Muhammed Ali Mehmood

I am a PhD student in Mathematics at Imperial College London, under the supervision of Prof. Ewelina Zatorska.

My research interests are centred around the analysis of PDE systems arising from (compressible) fluid mechanics which model complex flows such as traffic and multi-phase fluids (e.g. the Aw-Rascle model). I am also interested in the use of machine learning to study solutions to such models, particularly using Physics-Informed Neural Networks.

Prior to my PhD, I completed the MSc Pure Mathematics course at Imperial, and before that the BSc Mathematics at King's College London. You can view my MSc thesis here.

I am also broadly interested in quantitative finance and machine learning. On the projects page or my GitHub, you can find a few small projects that I’ve worked on.

CV  /  Scholar  /  GitHub

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Research

  1. Hard congestion limit of the dissipative Aw-Rascle system with a polynomial offset function
     Journal of Mathematical Analysis and Applications 533.1 (2024)
  2. Duality solutions to the hard-congestion model for the dissipative Aw-Rascle system
     With N. Chaudhuri, C. Perrin, and E. Zatorska,
    Communications in Partial Differential Equations (2024)
  3. Stability of partially congested travelling wave solutions for the extended Aw-Rascle system
     With É. Deléage, arXiv:2404.17406 (2024)
  4. Analysis of a Navier-Stokes Phase-Field Crystal Model
     With C. Cavaterra, M. Grasselli, and R. Voso,
    Nonlinear Analysis: Real World Applications (2024)

Awards