I am an Assistant Professor in the math department at the American University of Beirut. I received my BS in mathematics from NDU in 2016, my Master's in mathematics from AUB in 2018, and my Ph.D. in mathematics from Temple University in 2023. I worked at UCSB as a Visiting Assistant Professor for one and a half years. My research falls under analysis and PDEs and focuses on the mathematical analysis of deterministic and stochastic nonlinear and nonlocal systems of PDEs, describing the interactions of charged particles with fluids in the presence and absence of physical spatial boundaries. My work revolves around studying the global existence, uniqueness, regularity, long-time behavior, analyticity, and ergodicity of such models.

Here is my resume: Resume

Publications

23. E. Abdo, J. Germany, M. Hamdan, K. Kontar, Long-time dynamics of the Nernst-Planck-Darcy System on R^3, submitted. arXiv:2601.02208v1

22. E. Abdo, L. Chai, R. Hu, X. Yang, Convergence Analysis of PINNs for Fractional Diffusion Equations in Bounded Domains, submitted. arXiv:2601.01462

21. E. Abdo, Q. Lin, C. Tan, Well-posedness and Ill-posedness of the Primitive Equations with Fractional Horizontal Dissipation, submitted. arXiv:2508.12883

20. E. Abdo, Q. Lin, On the Dirichlet Fractional Laplacian and Applications to the SQG Equation on Bounded Domains, submitted. arXiv:2409.05209

19. E. Abdo, R. Hu, Q. Lin, On the Long-time Dynamics and Ergodicity of the Stochastic Nernst-Planck-Navier-Stokes System, submitted. arXiv:2310.20484 [math.AP]

18. E. Abdo, R. Hu, Q. Lin, On the Three-Dimensional Nernst-Planck-Boussinesq System, submitted. arXiv:2405.02152v1

17. E. Abdo, P. Constantin, M. Ignatova, Q. Lin, Electroconvection in a Magnetic Field, Discrete and Continuous Dynamical Systems - Series A, in honor of Professor Peter Lax's Centennial (2026). arXiv:2508.07439

16. E. Abdo, L. Chai, R. Hu, X. Yang, Error Estimates of Physics-Informed Neural Networks for Approximating Boltzmann Equations, IMA Journal of Numerical Analysis (2026). arXiv:2407.08383

15. E. Abdo, D. Nikolic, Long Time Dynamics of the Three-dimensional Nernst-Planck-Darcy Model, Nonlinearity (2025). arXiv:2408.07241

14. E. Abdo, Z. Hu, On the Space-Time Analyticity of the Keller-Segel-Navier-Stokes System, Journal of Nonlinear Science (2025). arXiv:2402.04564

13. E. Abdo, R. Hu, Q. Lin, Neural Network Solutions to the Critical SQG Equations via Approximating Nonlocal Periodic Operators, Physica D: Nonlinear Phenomena (2025). arXiv:2401.10879

12. E. Abdo, F-N. Lee, Logarithmic Sobolev Inequalities for Bounded Domains and Applications to Drift-Diffusion Equations, Journal of Functional Analysis (2025). arXiv:2402.18572

11. E. Abdo, M. Ignatova, Long Time Dynamics of a Fractional Dissipative Model of Electroconvection in Bounded Domains, Transactions of the AMS (2025). arXiv:2309.17423 [math.AP]

10. E. Abdo, On the Regularity of Solutions to some Active Scalar Equations on Bounded Domains, SIAM Journal on Mathematical Analysis (2024). paper

09. E. Abdo, W. Wang, On the Space-Time Analyticity of the Inhomogeneous Heat Equation on the Half-Space with Neumann Boundary Conditions, Applicable Analysis (2024). paper arXiv:2303.04713 [math.AP]

08. E. Abdo, M. Ignatova, Long Time Dynamics of Nernst-Planck-Navier-Stokes Systems, Journal of Differential Equations (2024). paper

07. E. Abdo, N. Glatt-Holtz, M. Ignatova, Unique Ergodicity in Stochastic Electroconvection, Nonlinear Differential Equations and Applications (2024). paper arXiv:2210.10600 [math.AP]

06. E. Abdo, M. Ignatova, Long Time Behavior of Solutions of an Electroconvection Model in R^2, Journal of Evolution Equations (2024). paper

05. E. Abdo, F-N. Lee, W. Wang, On the Global Well-Posedness and Analyticity of some Electrodiffusion Models in Ideal Fluids and Porous Media, SIAM Journal on Mathematical Analysis (2023). paper

04. E. Abdo, M. Ignatova, On Electroconvection in Porous Media, Indiana University Mathematics Journal (2023). paper

03. E. Abdo, M. Ignatova, On the Space Analyticity of the Nernst–Planck–Navier–Stokes System, Journal of Mathematical Fluid Mechanics (2022). paper

02. E. Abdo, M. Ignatova, Long Time Finite Dimensionality in Charged Fluids, Nonlinearity (2021). paper

01. E. Abdo, M. Ignatova, Long Time Dynamics of a Model of Electroconvection, Transactions of the AMS (2021). paper

E. Abdo, On the Nonlinear Interaction of Charged Particles with Fluids, PhD Dissertation (2023). http://dx.doi.org/10.34944/dspace/8837

E. Abdo, Extension of Biholomorphic Maps from Special Domains into their Boundaries, Master's Thesis (2018). http://hdl.handle.net/10938/21391

Teaching

American University of Beirut

MATH 202: Differential Equations (Spring 2025, Spring 2026)

MATH 210: Introduction to Real Analysis (Fall 2025)

MATH 212: Introductory Partial Differential Equations (Spring 2026)

University of California, Santa Barbara

MATH 6B: Vector Calculus with Applications (Fall 2023, Fall 2024)

MATH 8: Transition to Higher Mathematics (Spring 2024)

MATH 117: Methods of Analysis (Spring 2024)

MATH 118A: Introduction to Real Analysis 1 (Fall 2024)

MATH 118B: Introduction to Real Analysis 2 (Winter 2024)

Here are summarized student feedback forms for the courses that I taught: Evaluation Forms

Contact

Department of Mathematics

Faculty of Arts and Sciences

American University of Beirut

P.O. Box 11-0236

Riad El Solh,

Beirut 1107 2020

Lebanon

Email: ea94@aub.edu.lb

Instagram: Elie Abdo (@elieabdo24)

YouTube Channel: Elie Abdo - YouTube

Poetry Website: Elie Abdo - poet at allpoetry