American University of Beirut

Partial Differential Equations

​​​The mission of AUB-CAMS Partial Differential Equations Research Unit is to promote active and quality research related to the field. It aims at enhancing its members’ research and at strengthening the collaboration between active researchers within Lebanon and the region. 

The field of Partial differential equations (PDE’s) deals with an endless source of problems coming from modeling phenomena occurring in nature (mathematical physics, statistics, economy, mathematical biology, imaging sciences, etc.), which usually lead to challenging mathematical questions. Today, PDE’s constitute a vast field which can start with the formal or justified derivation of models up to numerical simulations that validate underlying mathematical models which encompass studying well-posedness, stability and if possible convergence of numerical solutions. Other properties of solutions can be dealt with such as: behavior in long time, blow-up in finite time, bifurcation profiles if any.

Over the past two decades, the Center for Advanced Mathematical Sciences has been at the core of a number of events focused on the area of PDE’s in close collaboration with various institutions in Lebanon, in particular, the Lebanese University. Notable events have taken place since 1997, including conferences, workshops, and lately symposia and thematic programs. 


Members


Founding members​

  • Ayman Kachmar is Professor at the Lebanese University. He specializes in semi-classical analysis and its connections to models in quantum mechanics and condensed matter physics, especially in the presence of magnetic fields.
  • Nabil Nassif is Professor at the American University of Beirut. His research focuses on analysis and simulation of PDE’s models arising in various application areas. His recent work deals with Numerical methods and inverse problems techniques in epidemiology, plasma physics, climatology, and medical sciences.
  • ​Raafat Talhouk​ is Professor at the Lebanese University. His research focuses on derivation and analysis of PDE’s models arising in mechanicalfluids and mathematical biology. His recent work concerns the derivation and mathematical analysis of asymptotic models in Shallow Water waves as well as the modeling and analysis of the electro-cardiac activity of the heart.

Select ​Publications


  • Ayman Kachmar 
    • ​B. Helffer, A. Kachmar. Quantum tunneling in deep potential wells and strong magnetic field revisited. arXiv:2208.13030.
    • A. Kachmar. M. Wehbe. Averaging of magnetic fields and applications. Commun. Contemp. Math. Vol. 25, No. 2, art. no. 2150108, 20 pp. (2023).
    • B. Helffer, A. Kachmar. Decay of superconductivity away from the magnetic zero set. Calc. Var. PDE. 56 (5) art. no. 130, 35 pp. (2017).

  • Nabil Na​ssif
    • ​​S. Moufawad, N. Nassif, Newton type methods for solving a Hasegawa–Mima plasma model, Applied Mathematics and Computation, (June 2023).
    • S. Moufawad, N. Nassif, F. Triki, Direct and Inverse Problem for Gas Diffusion in Polar Firn, arXiv: 2207.07352 (June 2023).
    • H. Karakazian, S. Moufawad, and N. Nassif. A Finite-Element Model for the Hasegawa-Mima Wave Equation, Applied Mathematics and Computation, 412 (1), January 2022.
    • N. Nassif, D. Sheaib, G. El Jannoun A Simulation Model for the Physiological Tick Life Cycle. Springer Proceedings in Mathematics and Statistics Modeling 2018 (273-284).

  • Raafat Talhouk
    • ​​A Miranville, W Saoud, R Talhouk, On the Cahn-Hilliard/Allen-Cahn equations with singular potentials.Discrete & Continuous Dynamical Systems-Series B 24 (8), 2019.
    • G Chamoun, M Saad, R Talhouk, Numerical analysis of a chemotaxis–swimming bacteria model on a general triangular mesh, Applied Numerical Mathematics 127, 324-348, 2018.
    • A Miranville, W Saoud, R Talhouk, Asymptotic behavior of a model for order-disorder and phase separation, Asymptotic Analysis 103 (1-2), 57-76, 2017.
    • V Duchêne, S Israwi, R Talhouk, A New Class of Two‐Layer Green–Naghdi Systems with Improved Frequency Dispersion. Studies in Applied Mathematics 137 (3), 356-415, 2016.

PDERU Associates


​TBA

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