My research interests lie in the fields of Calculus of Variations and Partial Differential Equations. More specifically, I work on some problems arising in Fluid Mechanics, Mean- Field Games, and Elasticity.
In Fluid Mechanics, I am interested in almost axisymmetric flows and both multidimensional compressible Euler and gas dynamics. Almost axisymmetric flows are important in Meteorology as they model tropical cyclones. From a theoretical point of view, these flows formally approximate the inviscid rotating hydrostatic Boussinesq equations from which they inherit the Hamiltonian structure. My work on the multidimensional compressible Euler equations and pressureless gas dynamics is devoted to the construction of variational scheme for measure-valued solutions and the description of related tangent spaces. The tools used in all these problems draw substantially on the theory of Optimal Mass Transport.
Recently, I have been interested in forward-forward Mean-Field Games which are variants of the standard Mean-field Games when the time is partially reversed. The forward -forward problem was proposed as a device to approximate stationary solutions of the standard Mean-Field Games. I am also working on a variational problem with a polyconvex integrand that comes from the study of gradient flows in Elasticity.
Publications
M. Sedjro, On the almost axisymmetric flows with forcing terms, dissertation 2012.
M. Cullen and M. Sedjro, On a model of forced axisymmetric flows. SIAM J. Math. Anal.,Vol. 46, No. 6, pp. 3983-4013, (2014).
M. Cullen, M. Sedjro, and W. Gangbo, A mathematically rigorous analysis of forced axisymmetric flows in the atmosphere. Quarterly J. Roy. Meteorol. Soc., Vol 141, Issue 690, Part A, pp 1836-1844, (2015).
F. Cavalletti, M. Sedjro, and M. Westdickenberg, A simple proof of a global existence of the 1 D pressureless gas dynamics equations. SIAM J. Math. Anal., Vol. 47, No. 1, pp 66-79, (2014).
M. Sedjro, A Monge-Ampere equation with an unusual boundary condition. Symmetry, 7(4), pp 2009-2024, (2015).
D. Gomes, L. Nuberkyan, and M. Sedjro, One-dimensional forward-forward Mean-Field Games. Appl. Math. Optim. Vol 74, No.3, pp 619-642, (2016)
F. Cavalletti, M. Sedjro, and M. Westdickenberg, A variational time discretization for the compressible Euler equations. (70 pages, Transactions of American Mathematical Society , accepted) (2018)_
D. Gomes, L. Nuberkyan, and M. Sedjro, Conservation laws arising in the study of forward-forward Mean-Field Games. (7 pages, accepted for publication in the proceedings of the XVI International Conference on Hyperbolic Problems)
M. Sedjro and M. Westdickenberg, Characterization of the tangent cone of monotone transport plans in R^d x R^d with prescribed first projection. (preprint, 24 pages).
R. Awi and M. Sedjro, On the uniqueness of minimizers for a class of variational problems with polyconvex integrands. ( Acta Applicandae Mathematicae pp 1-33).
D. Gomes and M. Sedjro, One-dimensional forward-forward Mean-Field Games with congestion. (14 pages, accepted for publication in DCDS-S).
M. Sedjro, On a model of axisymmetric flows in a free boundary domain (23 pages, preprint).
M. Sedjro Free boundary Monge-Ampere equations (19 pages, submitted).
M. Sedjro On the one-dimensional forward-forward Mean-Field Games with congestion. (9 pages, submitted)