• Dynamical Systems Weekend
• Stability Criteria for Multi-Dimensional Waves and Patterns
• International Internet Seminar
• Emerging Topics in Dynamical Systems and PDEs
  

VITA

List of Publications

Book:

• Evolution Semigroups in Dynamical Systems and Differential Equations. Math. Surv. Monogr.  70, AMS,  Providence, 1999. (with C. Chicone)

• Stability of gasless combustion fronts in one-dimensional solids, preprint (with A. Ghazaryn and S. Shechter) (PDF file)

• Perturbations of strongly continuous operator semigroups, and matrix Muckenhoupt weights, Functional Analysis and Its Applications, 42 (2008) 234-238 (with G. Gubreev) (PDF file)

• Derivatives of (Modified) Fredholm Determinants and Stability of Standing and Traveling Waves,  Journal de Mathematiques Pures et Appliquees, 90 (2008) 160-200 (with F. Gesztesy and K. Zumbrun)(PDF file)

• The spectral mapping property of delay semigroups, Complex Analysis Operator Theory, 2 (2008) 273–283 (with A. Batkai and T. Eisner)(PDF file)

• The Dichotomy Theorem for evolution bi-families, J. Differential Equations, 245 (2008) 2267-2306 (with A. Pogan)(PDF file)

• Center manifolds and dynamics near equilibria of quasilinear parabolic systems with fully nonlinear boundary conditions, Discrete Continuous Dynamical Systems B, 9 (2008) 595 - 633 (with J. Pruss and R. Schnaubelt)(PDF file)

• Scattering in a forked-shaped waveguide, Integral Eqns. Operator Theory, 61 (2008) 365-399 (with V. Pivovarchik)(PDF file)

• Stable and unstable manifolds  for quasilinear parabolic systems with fully nonlinear boundary conditions, J. Evolution Equations, 6 (2006) 535 - 576 (with J. Pruss and R. Schnaubelt)(PDF file)

• Dichotomy and Fredholm properties of evolution equations, J. Operator Theory, 58 (2007) 387 - 414 (with A. Pogan and R. Schnaubelt)(PDF file)

• Evans functions, Jost functions, and Fredholm determinants, Archive Ration. Mech. Anal., 182 (2007) 361 - 421 (with F. Gesztesy and K. A. Makarov) (PDF file)

• Non-self-adjoint operators, infinite determinants, and some applications,
  Russian J. Math. Phys. 12, No 4 (2005) 443-471 (with F. Gesztesy, M. Mitrea, and M. Zinchenko) (PDF file)

• Fredholm determinants and the Evans function for difference equations, Banach Center Publications, 75 (2007) 111-135 (with D. Cramer) (PDF file)

• Fredholm properties of evolution semigroups, Illinois J. Math., 48 (2004) 999-1020 (with Y. Tomilov) (PDF file)

• Regularization and frequency-domain stability of well-posed systems, Math. Control Signals Systems, 17 (2005) 128-151 (with T. Randolph and R. Schnaubelt) (PDF file)

• Fredholm differential operators with unbounded coefficients, J. Diff. Eqns., 208 (2005) 388-429 (with Y. Tomilov) (PDF file)

• Spectral analysis of Darboux transformations for the focusing NLS hierarchy, J. d'Anal. Math., 93 (2004) 139-197 (with F. Gesztesy, R. Cascaval, and H. Holden)  (PDF file)

• The essential spectrum of the linearized 2D Euler operator is a vertical band. Contemp. Math. 327 (2003) 299-304 (with R. Shvidkoy) (PDF file)

• Essential spectrum of the linearized 2D Euler equation and Lyapunov-Oseledets exponents, J. Math. Fluid. Mech.,  7 (2005) 164-178  (with R. Shvidkoy)   (PDF file)

• Linear stability in an ideal incompressible fluid. Comm. Math. Phys. 233 (2003) 439--461  (with M. Vishik) (PDF file)

• Operator valued Fourier multipliers and stability of strongly continuous semigroups, Integral Equations Operator Theory  51 (2005) 375-394  (with F. Raebiger) (PDF file)

• A sharp formula for the essential spectral radius of the Ruelle transfer operator on smooth and Holder spaces.  Ergod. Theory and Dynam. Syst. 23 (2003) 175-191 (with V. M. Gundlach) (PDF file)

• Gearhart-Pruss Theorem in stability for wave equations: a survey. In: Evolution Equations, G. Goldstein, R. Nagel, S. Romanelli (edts),  Lect. Notes Pure Appl. Math.  234 (with D. Cramer)  (PDF file)

• Hyperbolicity of semigroups and Fourier multipliers, In: Systems, Approximation, Singular Integral Operators,and Related Topics, International Workhop on Operator Theory and Applications, IWOTA 2000, eds. Alexander A. Borichev and Nikolai K. Nikolski,  Oper. Theory Adv. Appl. 129 (2001) 341--364 (with R. Shvydkoy). (PDF file)

• A spectral mapping theorem and invariant manifolds for nonlinear Schroedinger equations, Indiana Univ. Math. J.,  49  (2000) 221--243. (with F. Gesztezy, C. Jones, and M. Stanislavova). (PDF file)