Robert Pego

Professor
Ph.D., University of California, Berkeley

Office: 6130 Wean Hall
Phone: (412) 268-2553
E-mail: rpego AT cmu.edu
Personal Web Site:

Research

In general terms I work on nonlinear dynamics for infinite-dimensional physical systems. One focus of current work is the emergence of `universal' behavior in models of complex systems, particularly systems that exhibit clustering and coarsening phenomena. In recent work on basic models of coagulation, for example, we make use of remarkable connections between probability and dynamical systems theory to carry out a rather complete dynamic analysis, revealing universal convergence to self-similar form in some regimes, signs of chaos in others.

Other areas of special interest concern nonlinear waves, emphasizing stability issues in dynamics and for computation. Nonlinear waves are important features in numerous physical models of fluids (both classical and quantum), plasmas, and elastic bodies. One aim is to understand why solitary waves in many Hamiltonian systems are stable. A classic example that is still poorly understood is the solitary water wave famously followed on horseback by J. Scott Russell in 1834.

Selected Publications

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

J.-G. Liu, J. Liu and R. L. Pego, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Comm. Pure Appl. Math. 60 (2007) 1443-1487.

G. Menon and R. L. Pego, Approach to self-similarity in Smoluchowski's coagulation equations, Comm. Pure Appl. Math. 57 (9) (2004) 1197--1232.

G. Friesecke and R. L. Pego, Solitary waves on Fermi-Pasta-Ulam lattices IV: Proof of stability at low energy, Nonlinearity 17 (2004) 229--251.

R. L. Pego and J. R. Quintero, A host of traveling-wave solutions for a model of three-dimensional water-wave dynamics, J. Nonl. Sci. 12 (2002) 59--83.

B. Niethammer and R. L. Pego, Non-self-similar behavior in the LSW theory of Ostwald ripening, J. Stat. Phys. 95 (1999) 867--902.