# Robert Pego

## Professor Emeritus

**Address:**

6127 Wean Hall

Department of Mathematical Sciences

Carnegie Mellon University

5000 Forbes Avenue

Pittsburgh, PA 15213

**P:** 412-268-2545

# Education

Ph.D. in Applied Mathematics, University of California, Berkeley

# Awards

- Simons Foundation Fellowship
- Fellow of the American Mathematical Society
- SIAM Fellow

# Research

My research concerns nonlinear dynamics in partial differential equations, especially coherent structures and nonlinear waves. One focus is to explain the emergence of universal scaling behavior in models of clustering and coarsening, stability of nonlinear waves and coherent states. Recent work on self-similar structures in kinetic models of coagulation has established some remarkable rigorous connections to random shock dynamics (Burgers turbulence model), Levy-Khintchine formulae, and the classic theory of branching processes in probability theory.

Work on solitary waves has achieved proofs of linear stability for the full Euler equations of water waves without surface tension, and nonlinear asymptotic stability for a prototypical model with the same infinitely indefinite variational structure.

Another line of research concerns how to pose correct boundary conditions for the pressure in the Navier-Stokes equations for viscous, incompressible flow with no slip on the boundary. A new theory was developed proving that a particular commutator formula provides a correct and stable pressure, and new high-performing numerical schemes were proposed based on it.

Ongoing investigations involve coagulation-fragmentation models of sticky particles and animal groups, and Bose-Einstein condensation in a model equation arising in kinetic theory for Compton scattering of photons.

# Select Publications

Degond, P., Liu, J.-G., and Pego, R. L. (2017). Coagulation-fragmentation model for animal group-size statistics. *J. Nonlinear Sci.*, 27, 379-424.

Pego, R.L. (2017, Apr). How to count fish using mathematics. *SIAM News*. https://sinews.siam.org/Details-Page/how-to-count-fish-using-mathematics.

Murray, R.~W. and Pego, R.L. (2017). Cutoff estimates for the Becker-Doring equations. *Comm. Math. Sci.,* 15, 1685-1702.

Pego, R. L. and Sun, S.-M. (2016). Asymptotic linear stability of solitary water waves. *Arch. Rational Mech. Anal.*, 222, 1161-1216.

Ballew, J., Iyer, G. and Pego, R. L. (2016). Bose-Einstein condensation in a hyperbolic model of the Kompaneets equation. *SIAM J. Math. Anal.,* 48, 3840-3859.

Liu, J.-G. and Pego, R. L. (2016). On generating functions for Hausdorff moment sequences. *Trans. Amer. Math. Soc.* 368, 8499-8518.

Iyer, G., Leger, N. and Pego, R. L. (2015). Limit theorems for Smoluchowski dynamics associated with critical continuous-state branching processes. *Ann. Appl. Probab.*, 25, 675-713.

Mizumachi, T., Pego, R. L. and Quintero, J. R. (2013). Asymptotic stability of solitary waves in the Benney-Luke model of water waves. *Diff. Int. Eq.,* 26, 253-301*.*

Liu, J.-G., Liu, J. and Pego, R. L. (2010). Stable and accurate pressure approximation for unsteady incompressible viscous flow.* J. Comp. Phys.* 229, 3428-3453.

Menon, G. and Pego, R. L. (2008). The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations. J. Nonl. Sci., 18, 143-190.

Sprauge, B., Pego, R.L., Stavrea, D. A. and McNally, J. G. (2004). FRAP analysis in the presence of binding. *Biophys. J.*, 86, 3473-3495.