Urbana, IL 61801
Partial Differential Equations, Nonlinear Analysis
I currently work on existence and stability of coherent structures (bound states, solitons, kinks) in Hamiltonian equations and their interaction and coupling with radiation under deterministic and random perturbation. More generally I am interested in hyperbolic and dispersive waves in inhomogeneous and random media and in developing variational and fixed point methods for nonlinear equations to study the existence, stability of solutions and their bifurcations.
Kirr, E. (2017). Long time dynamics and coherent states in nonlinear wave equations. In Fields Institute Communications (pp. 59-88). (Fields Institute Communications; Vol. 79). Springer. https://doi.org/10.1007/978-1-4939-6969-2_3
Kirr, E., Wilkinson, M., & Zarnescu, A. (2014). Dynamic Statistical Scaling in the Landau-de Gennes Theory of Nematic Liquid Crystals. Journal of Statistical Physics, 155(4), 625-657. https://doi.org/10.1007/s10955-014-0970-6
Kirr, E., Kevrekidis, P. G., & Pelinovsky, D. E. (2011). Symmetry-Breaking Bifurcation in the Nonlinear Schrödinger Equation with Symmetric Potentials. Communications in Mathematical Physics, 308(3), 795-844. https://doi.org/10.1007/s00220-011-1361-3
Kirr, E., & Zarnescu, A. (2009). Asymptotic stability of ground states in 2D nonlinear Schrödinger equation including subcritical cases. Journal of Differential Equations, 247(3), 710-735. https://doi.org/10.1016/j.jde.2009.04.015
Kirr, E., & Mizrak, Ö. (2009). Asymptotic stability of ground states in 3D nonlinear Schrödinger equation including subcritical cases. Journal of Functional Analysis, 257(12), 3691-3747. https://doi.org/10.1016/j.jfa.2009.08.010