Eduard-Wilhelm Kirr

Research interests:

• Existence and stability of coherent structures (bound states, solitons, kinks) in Hamiltonian equations. Their interaction and coupling with radiation under deterministic and random perturbation
• Hyperbolic and dispersive waves in inhomogeneous and random media
• Variational and fixed point methods for nonlinear equations. Existence, stability of solutions and bifurcations

Publications and Preprints:

1. Asymptotic stability of ground states in 2D nonlinear Schroedinger equation including subcritical cases
   (with Zarnescu, A.) submitted to J. Diff. Eq.
2. Asymptotic stability of ground states in 3D nonlinear Schroedinger equation including subcritical cases
   (with Mizrak, O.) submitted to J. Funct. Anal.
3. Symmetry breaking bifurcation in Nonlinear Schroedinger /Gross-Pitaevskii Equations
   (with Kevrekidis P.G., Shlizerman E. and Weinstein M.I.) to appear in SIAM J. Math. Anal.
4. On the asymptotic stability of bound states in 2D cubic Schroedinger equation
   (with Zarnescu, A.) Comm. Math. Phys. 272 (2007), no. 2, 443--468
5. Parametric resonance of ground states in the nonlinear Schroedinger equation
   (with Cuccagna, S. and Pelinovsky, D.) J. Differential Equations 220 (2006), no. 1, 85--120.
6. Diffusion of power in randomly perturbed Hamiltonian partial differential equations
   (with Weinstein, M.I.) Comm. Math. Phys. 255 (2005), no. 2, 293--328.
7. Compressible Two-Phase Flows by Central and Upwind Schemes
   (with Karni S.; Kurganov A. and Petrova G.) ESAIM:M2AN 38 (2004) no. 3, 477-493.
8. Metastable states in parametrically excited multimode Hamiltonian systems
   (with Weinstein, M.I.) Commun. Math. Phys., 236 (2003), no. 2, 335-372
9. Resonances in Parametrically Excited Hamiltonian Partial Differential Equations
   Ph. D. Thesis, University of Michigan, 2002
10. Parametrically excited Hamiltonian partial differential equations
    (with Weinstein, M.I.) SIAM. J. Math. Anal. 33 (2001), no. 1, 16--52
11. Periodic solutions of superlinear impulsive differential systems
    (with Precup, R.) Commun. Appl. Anal. 3 (1999), no. 4, 483--502
12. Continuous dependence on parameters of the fixed points set for some set-valued operators
    (with Petrusel, A.) Discuss. Math. Differential Incl. 17 (1997), no. 1-2, 29--41
13. Periodic solutions for perturbed Hamiltonian systems with superlinear growth and impulsive effects
    Studia Univ. Babes-Bolyai Math. 41 (1996), no. 4, 55--65
14. Existence and continuous dependence on data of the positive solutions of an integral equation from biomathematics
    Studia Univ. Babes-Bolyai Math. 41 (1996), no. 2, 59--72
15. Existence of periodic solutions for some integral equations arising in infectious diseases
    Studia Univ. Babes-Bolyai Math. 39 (1994), no. 2, 106--119
16. Continuous dependence and fixed points for some multivalued operators
    (with Petrusel, A.) Rev. Anal. Numer. Theor. Approx. 26 (1997), no. 1-2, 99--101

Invited Lectures:

• Univ. of Illinois at Urbana-Champaign -- Harmonic Analysis Seminar, 10/2007
• AMS Sectional Meeting, Chicago, IL Special session on Wave Propagation from Mathematical and Numerical View Points -- Gabriel Koch organizer, 10/2007
• SIAM Conference on Dynamical Systems, Snowbird, Utah, Special session on Non-integrable Phenomena in NLS -- Avraham Soffer organizer, 05/2007
• Northern Illinois University, Dekalb, IL -- Colloquium, 11/2006
• Banff International Research Station, Banff, Canada -- Workshop on Evolution of Microscopic and Macroscopic Fields, 09/2006
• Univ. of Illinois at Urbana-Champaign -- New Faculty Seminar, 10/2005
• Univ. of Illinois at Urbana-Champaign -- Harmonic Analysis Seminar, 09/2005
• SIAM Conference on Dynamical Systems, Snowbird, Utah, Special session discrete and continuous models in nonlinear optics -- Milena Stanislavova organizer, 05/2005
• Argonne National Laboratory -- Mathematics and Computer Science Division Seminar, 04/2005.
• Univ. of California at Davis, Univ. of Utah, Oklahoma State Univ., Univ. of Kansas, Georgia Tech University, Univ. of South Carolina -- Colloquium, 01-02/2005.
• University of Illinois at Urbana-Champaign -- Stochastic and Nonlinear Analysis Seminar, 10/2004
• University of Massachusetts at Amherst -- Applied Analysis and Computation Seminar, 10/2004
• International Conference on Nonlinear Differential Equations and Applications Cluj, Romania, 08/2004
• AIMS' Fifth International Conference, Pomona, CA, Special session on wave propagation and inverse problems -- Guillaume Ball, organizer, 06/2004
• University of California at Davis -- Applied Mathematics Seminar, 06/2004
• The Fields Institute, Toronto -- Workshop on Integrable and Near-integrable Hamiltonian PDE, 05/2004
• The Fields Institute, Toronto -- Workshop on Resonances in Linear and Nonlinear Schr\" odinger Equation, 08/2003
• University of Utah Workshop on waves in inhomogeneous media, 08/2003
• University of Michigan at Ann Arbor -- Department of Mathematics Colloquium,03/2003
• University of Chicago-- CAMP/Nonlinear PDE seminar, 10/2002
• Mt. Holyoke, MA -- Workshop on Waves in Periodic and Random Media, 06/2002
• University of Colorado at Boulder -- Applied Mathematics Seminar, 02/2002
• University of Illinois at Chicago -- Mathematics and its applications seminar, 01/2002
• Bell Laboratories, Murray Hill, NJ -- Numerical Analysis Seminar, 07/2000
• ICMS Edinburgh, UK -- Workshop on Hamiltonian Mechanics and Small Divisors in PDE, 05/1999
• Second Joint Conference on Modern Applied Mathematics, Ilieni, Romania, 05/1997
• Troisieme Colloque Franco-Roumain, Cluj, Romania, 05/1996
• National Conference on Differential Equations, Cluj, Romania, 04/1996