Jinqiao Duan's Recent Publications

      Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA.      E-mail: duan@iit.edu

 

Books:

E. Waymire and J. Duan (Eds.) --- 

Probability and Partial Differential Equations in Modern Applied Mathematics.  Springer-Verlag,  2005.

 

Papers on Stochastic Dynamics & Stochastic Partial Differential Equations:

  • J. Duan and A. Millet, Large deviations for the Boussinesq equations under random influences.    Submitted, 2007.
  • D. Blomker and J. Duan, Predictability of the Burgers dynamics under model uncertainty (PDF). In Boris Rozovsky 60th birthday volume  Stochastic Differential Equations: Theory and Applications, P. Baxendale and S. Lototsky (Eds.), p.71-90, World Scientific, New Jersey, 2007.
  • L. Wan and J. Duan, Exponential stability of non-autonomous stochastic partial differential equations with finite memory  (PDF). Statistics & Probability Letters, in press, 2007.
  • W. Wang and J. Duan, Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions (PDF).  Comm. Math. Phys. 275  (2007), 163-186.
  • D. Yang and J. Duan, An impact of stochastic dynamic boundary conditions on the evolution of   the Cahn-Hilliard system (PDF).  Stochastic Analysis and Applications  25 (2007), 613-639.
  • W. Wang, D. Cao and J. Duan, Effective macroscopic dynamics of stochastic partial differential equations in perforated domains (PDF). SIAM J. Math. Anal.  38 (2007), 1508-1527.
  • W. Wang and J. Duan, A dynamical approximation for stochastic partial differential equations (PDF).   J. Math. Phys., 48, No. 10, 2007.
  • A. Du and J. Duan, Invariant manifold reduction for stochastic dynamical systems (PDF).  Dynamical Systems and Applications 16 (2007),  681-696.
  • J. Duan, K. Lu and B. Schmalfuss, Invariant manifolds for stochastic partial differential equations (PDF). Annals of Probability 31(2003), 2109-2135.
  • J. Duan, K. Lu and B. Schmalfuss, Stable and unstable manifolds for stochastic partial differential equations (PDF).  J. Dynamics and Diff. Eqns 2004, Vol. 16, No. 4, 949-972.
  • C. Gugg and J. Duan, A Markov jump process approximation of the stochastic Burgers equation (PDF). Stochastics and Dynamics  4(2004),  No. 2, 245-264.
  • W. Wang, J. Sun and J. Duan, Ergodic Dynamics of the Stochastic Swift-Hohenberg System (PDF). Nonlinear Analysis B, 6  (2005), 273-295.
  • I. Chueshov, J. Duan and B. Schmalfuss, Determining functionals for random partial differential equations (application to stochastic Navier-Stokes equations) (PDF). Nonlinear Diff. Eqns. Appl. (NoDEA)  10(2003), 431-454.
  • Fractional Fokker--Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises (PDF), with D. Schertzer, M. Larcheveque, V.V.Yanovsky and S. Lovejoy, J. Math. Phys., 42(2001), 200-212.
  • J. Duan and V. J. Ervin, On the Stochastic Kuramoto-Sivashinsky Equation,   Nonlinear Analysis, 44(2001), 205-216.

 

Papers on Stochastic & Computational Approaches for Multiscale and Random   Phenomena: 

  • J. Duan  and B. Nadiga. Stochastic parameterization for large eddy simulation of geophysical flows  (PDF).  Proc. Amer. Math. Soc. 135 (2007), 1187-1196.
  • J. Duan and A. V. Fursikov, Feedback stabilization  for Oseen fluid equations: A stochastic approach (PDF). J. Math. Fluid Mech., 7 (2005), 574 - 610.
  • V. P. Bongolan-Walsh,  J. Duan,  P.  Fischer, T.  Ozgökmen and T. Iliescu. Impact of Boundary Conditions on Entrainment and Transport in Gravity Currents (PDF).  Applied Mathematical Modelling,  31 (2007),   1338-1350.
  • V. P. Bongolan-Walsh, J. Duan, and T. Ozgokmen. Dynamics of Transport under Random Fluxes on the Boundary (PDF). Communications in Nonlinear Science and Numerical Simulation, online version available doi:10.1016/j.cnsns.2006.09.019, 2006.
  • T. Ozgokmen,  T. Iliescu, P. Fischer, A. Srinivasan  and J. Duan.  Large eddy simulation of stratified mixing in two-dimensional dam-break problem in a rectangular enclosed domain (PDF). Ocean Modeling, 16 (2007), 106-140.
  • A. Du,  J. Duan, H. Gao, and T. Ozgokmen.   Ergodic dynamics of the coupled quasi-geostrophic and energy balance system (PDF). Fundamental and Applied Math. (Moscow),  12 (2006),  No. 6 , 67-84.
  • T. Ozgokmen, P. Fischer, J. Duan and T. Iliescu, Entrainment in Bottom Gravity Currents Over Complex Topography from Three-Dimensional Non-hydrostatic Simulations (PDF).   Geophysical Research Letters, 31(2004), L13212.
  • T. Ozgokmen, P. Fischer, J. Duan and T. Iliescu, Three-Dimensional Turbulent Bottom Density Currents From a High-Order Non-hydrostatic Spectral Element Model (PDF).   Journal of Physical Oceanography, 34(2004), 2006-2026.
  • J. Duan, H.Gao and B. Schmalfuss, Stochastic dynamics of a coupled atmosphere-ocean model (PDF). Stochastics and Dynamics, Vol 2, No. 3, 2002, 357-380.
  • J. Duan and B. Schmalfuss, The 3D Quasigeostropic Fluid Dynamics under Random Forcing on Boundary (PDF). Comm. in Math. Sci. , Vol 1, No 1, 2003, 133-151.
  • D. Blomker, J. Duan and T. Wanner, Enstrophy Dynamics of Stochastically Forced Large-Scale Geophysical Flows (PDF). J. Math. Phys., 43 (2002), 2616-2626.
  • J. Duan, P. E. Kloeden and B. Schmalfuss, Exponential Stability of the Quasigeostrophic Equation under Random Perturbations (PDF). Progress in Probability  49(2000), 241-256.
  • J. Duan and B. Goldys, Ergodicity of Stochastically Forced Large Scale Geophysical Flows (PDF). Inter. J. Math. Math. Sci., 28 (2001), 313-320.
  • I. Chueshov, J. Duan and B. Schmalfuss, Probabilistic Dynamics of Two-Layer Geophysical Flows (PDF). Stochastics and Dynamics, Vol 1, No. 4, 2001.
  • Escape Probability, Mean Residence Time and Geophysical Fluid Particle Dynamics (PDF), with J. Brannan and V. J. Ervin, Physica D 133 (1999), 23--33.
  • Dissipative Quasigeostrophic Motion under Temporally Almost Periodic Forcing, with Peter Kloeden, J. Math. Anal. Appl. 236 (1999), 74-85.
  • Variational Methods and Nonlinear Quasigeostrophic Waves (PDF), with D. D. Holm and K. Li, Physics of Fluids 11(1999), 875-879.
  • Lagrangian transport and chaos in the near wake of the flow around an obstacle: a numerical implementation of lobe dynamics (PDF), with S. Wiggins, Nonlinear Processes in Geophysics 4 (1997), 125-136.
  • Fluid exchange across a meandering jet with quasiperiodic variability (PS), with S. Wiggins, J. Physical Oceanography 26 (1996), 1176-1188.
  • Nonlinear stability of one-layer geostrophic fronts (PDF), with S. Wiggins, Physica D, 98 (1996), 335-342.

 

Papers on Nonlinear and Nonautonomous Dynamics:

  • Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity (PDF), by Chunyou Sun, Daomin Cao, Jinqiao Duan,  Nonlinearity  19 (2006), 2645-2665.
  • Uniform attractors for non-autonomous wave equations with nonlinear damping (PDF), by Chunyou Sun, Daomin Cao, Jinqiao Duan,  SIAM J. Applied Dynamical Systems, 6 (2007), 293-318.
  • C. Sun, D. Cao and J. Duan, Non-autonomous wave dynamics with memory: Asymptotic regularity and uniform attractor.  Discrete and Continuous Dynamical Systems,  in press, 2007.
  • J. Duan, C. Potzsche and S. Siegmund, Slow integral manifolds for Lagrangian fluid dynamics in unsteady geophysical flows (PDF). Physica D, 233 (2007), 73-82.
  • X. Fu and J. Duan, Global attractors and invariant measures for non-invertible planar piecewise isometric maps. Phys. Lett. A,  to appear, 2007.
  • D. Cheban and J. Duan, Almost Periodic Motions and Global Attractors of the Nonautonomous Navier-Stokes Equations (PDF). J. Dynamics and Diff. Eqns., 16 (2004), 1--34.
  • V. P. Bongolan-Walsh, D. Cheban and J. Duan, Recurrent Motions in the Nonautonomous Navier-Stokes System (PDF).  Discrete and Continuous Dyn. Sys. B, No.3, 2002, 255-262.
  • X. Fu, W. Lu, P. Ashwin and J. Duan, Symbolic Representations of Iterated Maps  (PDF), Topological Methods in Nonlinear Analysis, 18 (2001), 119-147.
  • Infinite-dimensional linear dynamical systems with chaoticity, with X. Fu, J. Nonlinear Sci., 9 (1999), 197-211.
  • Chaotic Properties of Subshifts Generated by a Non-periodic Recurrent Orbit, with R. S. MacKay, X. Fu and Y. Fu, Inter. J. Bifurcation and Chaos, 10(2000), 1067-1073.
  • Asymptotic Dynamical Difference between the Nonlocal and Local Swift-Hohenberg Models (PDF), with G. Lin, H. Gao and V. Ervin, J. Math. Phys. , 41(2000), 2077-2089.
  • Dynamics of a nonlocal Kuramoto-Sivashinsky equation (PDF), with Vince Ervin, J. Diff. Eqns., 143(1998), 243-266. 
  • The effect of nonlocal interactions on the dynamics of the Ginzburg-Landau equation  (PDF), with H. Ly and E. S. Titi, Z. Angew. Math. Phys. 47 (1996), 433-455.
  • Fronts, domain walls and pulses for a generalized Ginzburg-Landau equation  (PDF), with P. Holmes, Proc. Edinburgh Math. Soc. 38(1995), 77-97.