AbdulRahman Alharbi

Biography

AbdulRahman Mohammad Alharbi is a Ph.D. candidate in Applied Mathematics at King Abdullah University of Science and Technology (KAUST), working under the supervision of Professor Diogo Gomes. His primary area of research focuses on first-order mean-field games on bounded domains, with an emphasis on entry-exit flow constraints, contact-set conditions, and the analytical challenges posed by nonstandard boundary behavior.

AbdulRahman received his M.S. degree in Applied Mathematics from KAUST in 2019, with a thesis exploring the Lp-integrability of Green’s functions for elliptic differential operators. Prior to that, he received his BA in Mathematics from Rutgers University with a minor in Physics in 2017.

In addition to his research, AbdulRahman has held teaching roles at KAUST and the Islamic University of Madinah, assisting in courses on calculus, linear algebra, and partial differential equations at both undergraduate and graduate levels. He has also participated in and presented his research at international and local conferences, including the American Institute of Mathematical Sciences (AIMS ) Conference on Dynamical Systems, the conference of the S ITE center hosted by NYU Abu Dhabi, and the CMSA conference hosted by the Saudi Association of Mathematics (SAM).

His most recent work examines the well-posedness of MFG systems with nonstandard mixed boundary conditions, variational formulations of MFGs, the local regularity of weak solutions, and the monotone operator structure underlying such systems. These topics lie at the interface of partial differential equations, variational analysis, and optimal control.