Ross Hall, Room 202
1000 E. University Ave.
Laramie, WY 82071
Research interests: Applied analysis and partial differential equations: nonlinear waves, existence & stability of traveling waves, Evans-function techniques, conservation & balance laws, gas dynamics, shock waves, combustion, integrable equations.
Department of Mathematics
University of Wyoming
Ross Hall 230
Ph.D., Indiana, 2002
I grew up in Fort Wayne, Indiana (the one-time magnet wire capital of the world), and I earned a BA in mathematics from St. Olaf College. My PhD is from Indiana University, Bloomington. After a post-doctoral stint at the University of Michigan, I came to Wyoming in 2005. Outside of mathematics, I enjoy skiing, ruminating on the New York Times crossword puzzle, drinking good coffee, and passionately following the (mis)fortunes of the Indiana University men's basketball team.
My mathematical interests are primarily in partial differential equations. At the heart of most of my work is the desire to understand the behavior of solutions of certain nonlinear partial differential equations which arise as models of physical phenomena. These investigations typically employ various techniques and ideas from rigorous real, complex, and functional analysis; numerical computation; dynamical systems; and modern asymptotic methods. Indeed, many of my research projects combine elements from several or all of these mathematical disciplines.
L. Lee, G. Lyng, and I. Vankova, The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schrödinger equation, Physica D, 241 (2012): 1767 - 1781. DOI: 10.1016/j.physd.2012.08.006
J. Humpherys, G. Lyng, and K. Zumbrun, Spectral stability of ideal-gas shock layers, Archive for Rational Mechanics and Analysis, 194 (2009): 1029 - 1079. DOI: 10.1007/s00205-008-0195-4
G. Lyng, M. Raoofi, B. Texier, and K. Zumbrun, Pointwise Green function bounds and stability of combustion waves, Journal of Differential Equations, 233 (2007): 654 - 698. DOI: 10.1016/j.jde.2006.10.006
G. Lyng and P. D. Miller, The N-soliton of the focusing nonlinear Schrödinger equation for N large, Communications on Pure and Applied Mathematics, 60 (2007): 951 - 1026. DOI: 10.1002/cpa.20162
H. K. Jenssen, G. Lyng, and M. Williams, Equivalence of low-frequency stability conditions for multidimensional detonations in three models of combustion, Indiana University Mathematics Journal, 54 (2005): 1 - 64. DOI: 10.1512/iumj.2005.54.2685