Research Interest : Nonlocal PDEs, Stochastic dynamical systems, and their applications
  1. Spectral theory of nonlocal operator

  2. Numerical methods for Nonlocal PDEs

  3. Stochastic differential equations in physical and chemical systems

  4. Population model in biology and ecology

Publications
  1. X. Xie, J. Duan, X. Li, and G. Lv. A regularity result for the fractional Fokker-Planck equation with Ornstein-Uhlenbeck drift,preprint arXiv:1504.04631

  2. W.Shen and X.Xie. Spectral theory for nonlocal dispersal operators with time periodic indefinite weight functions and applications (submitted)

  3. W.Shen and X.Xie. Approximation of Random Dispersal Operators by Nonlocal Dispersal Operators Journal of Differential Equations, 259 (2015), no. 12, 7375-7405.

  4. W.Shen and X.Xie. On principal spectrum points/principal eigenvalues of nonlocal dispersal operators and applications Discrete and Continuous Dynamical Systems-Series A, 35 (2015), no. 4, 1665-1696.

  5. L.Zhao, P.Zhao and X.Xie. Existence and multiplicity of solutions for divergence type elliptic equations. Electronic Journal of Differential Equations, Vol.2011(2011), No.43, pp.1-9

Work in process
  1. X.Xie. Classical, Nonlocal and Fractional Dispersal Operators and Connections to the Winner, Compound Poisson and L'evy Processes.

  2. X.Xie and X.Li. Numerical Method for the nonlocal operators with singular kernel and applications in Fokker-Planck equations on bounded domain

  3. W.Shen and X.Xie. Minimization of the generalized principal eigenvalue for nonlocal boundary value problem with indefinite weight, and applications to population dynamics

  4. J.Coville and X.Xie. Persistence criteria in time periodic environment for populations with non-local dispersion

  5. X. Xie, J. Duan, and X. Li. A regularity result for the fractional Fokker-Planck equation with Ornstein-Uhlenbeck drift with Dirichlet boundary condition

Conference Presentations
  1. Invited Talk, the 11th AIMS Conference on Dynamical Systems,Differential Equations and Applications Orlando, FL,  Jul.2016

  2. Invited Talk, at the Special Session \textit{Random and Complex Dynamics of Reaction-Diffusion Systems, I at the 2016 Joint Mathematics Meeting Seattle, WA.  Jan.2016

  3. Invited Talk, at the East Lake International Forum for Outstanding Oversees Young Scholars Huazhong University of Science and Technology Wuhan, Hubei,China  Dec.2015

  4. Poster Presentation, the Nonlocal Models in Mathematics, Computation, Science, and Engineering Oak Ridge National Laboratory, Oak Ridge, TN.  Oct.2015

  5. Invited Talk, the 35th Southeastern Atlantic Regional Conference on Differential Equations University of North Carolina at Greensboro, Greensboro, NC.  Oct.2015

  6. Co-Organizer and Invited Talk, at the Special Session Nonlocal Diffusion the AMS Central Fall Sectional Meeting Loyola University Chicago, Chicago, IL.  Oct.2015

  7. Invited Talk, the Workshop on Mathematical Biology and Nonlinear Analysis University of Miami, Coral Gables, FL.  Dec.2014

  8. Invited Talk, at the Special Session Reaction Diffusion Equations and Applications at the 2014 Joint Mathematics Meeting, Baltimore,MD,  Jan.2014

  9. Invited Talk, at the 9th Annual UNCG Regional Mathematics and Statistics Conference, University of North Carolina at Greensboro,Greensboro,NC,  Nov.2013

  10. Seminar Talk, at the Applied and Computational Mathematics Seminar, Department of Mathematics and Statistics, Auburn University, Auburn, AL,  Sep.2013

  11. Seminar Talk, at the Graduate Student Seminar, Department of Mathematics and Statistics, Auburn University, Auburn, AL,  Sep.2013

  12. Poster Presentation, in the IMA Annual Program Year Workshop: Lattice and Nonlocal Dynamical Systems and Applications, IMA (Institute of Mathematics and its Applications), Minneapolis, MN,  Dec.2012

  13. Invited Talk, at Special Session Dissipative Systems and Applications at t the 9th American Institute of Mathematical Sciences Conference on Dynamical Systems, DifferentialEquations and Applications, Orlando, FL,  Jul.2012

  14. Poster Presentation, in the SAMSI summer program: Nonlocal Continuum Models for Diffusion, Mechanics, and Other Applications, SAMSI(Statistical and Applied mathematical Sciences Institute), Research Triangle Park, NC Jun.2012

  15. Poster Presentation, at the 36th Annual SIAM (Society for Industrial and Applied Mathematics) Southeastern Atlantic Section Conference, Huntsville,AL Mar.2012

  16. Invited Presentation, at the 60th Annual Meeting of the Alabama Association of College Teachers of Mathematics Tuskegee,AL Feb.2010