His work has featured contributions to the theory and computation of Partial differential equations with diverse applications to shock wave, kinetic transport, incompressible flows, image processing, and self-organized collective dynamics.

He returned to his alma mater, and held professorship positions at Tel-Aviv University during 1983–1998, where he chaired the Department of Applied Mathematics (1991–1993).

He moved to UCLA (1995–2002), where he was the founding co-director of the NSF Institute for Pure and Applied Mathematics (IPAM) (1999–2001).

In 2012 he was awarded as the PI of the NSF Research network "Kinetic Description of Emerging Challenges in Natural Sciences" (KI-Net) (2012–2018).

[citation needed] He has given an invited lecture at the 2002 International Congress of Mathematicians (ICM) (Beijing), plenary addresses in the international conferences on hyperbolic problems (Zürich 1990 and Beijing 1998), and the 2008 Foundations of Computational Mathematics meeting in Hong Kong, and the SIAM invited address at the 2014 Joint Mathematical meeting in Baltimore.