• 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 estimates for  semigroups on Banach spaces, preprint (with A. V. Yurov) (PDF file)
• The Evans function and the Weyl-Titchmarsh function, Discr. Cont. Dynam. Systems,  to appear (with A. Sukhtayev) (PDF file)
• The infinite dimensional Evans function, preprint (with A. Pogan) (PDF file)
• Derivatives of the Evans function and (modified) Fredholm determinants for first order systems, Mathematische Nachrichten, 284 (2011) 1592 - 1638 (with M. Das) (PDF file)

• Functional models of non-selfadjoint operators, strongly continuous semigroups, and matrix Muckenhoupt weights, Izvestiya : Mathematics 75:2 (2011) 287–346 (with G. M. Gubreev) (PDF file)
• The index formula and the spectral shift function for relatively trace class perturbations, Advances in Mathematics 227 (2011) 319–420 (with F. Gesztezy, K. A. Makarov, F. Sukochev and Y. Tomilov) (PDF file)

• Stability of traveling waves for a class of reaction-diffusion systems that arise in chemical reaction models, SIAM J. Mathematical Analysis 42 (2010) 2434 - 2472 (with A. Ghazaryan and S. Schecter) (PDF file)
• Stability of traveling waves for degenerate systems of reaction diffusion equations, Indiana University Math. J., to appear (with A. Ghazaryan and S. Schecter) (PDF file)
• The algebraic multiplicity of eigenvalues and the Evans function revisited, Mat. Model. Nat. Phenom. 5 (2010)  269 - 292 (with A. Sukhtayev) (PDF file)
• Operator algebras and the Fredholm spectrum of advective equations of linear hydrodynamics, Journal of Functional Analysis, 257 (2009) 3309–3328 (with R. Shvydkoy) (PDF file)
• Stability of gasless combustion fronts in one-dimensional solids, Archive Ration. Mech. Anal. 198 (2010) 981-1030. (with A. Ghazaryan, S. Schecter, and A. de Souza) (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)