Research Interest

    A common sense definition of a dynamical system is any phenomenon of nature evolving in time. A particular class of dynamical systems described by partial differential equations (PDEs) contains a huge variety of problems in sciences and engineering. Their common feature is that they are governed by their own PDEs. 
      Specific questions of the qualitative theory of dynamical systems induced by PDEs are: long time behavior of solutions and stability problem. Local stability analysis leads to deep problems about the spectrum of the linearized operators while the existence and topological structure of global attractors and inertial manifolds are typical goals in the global stability setting.
        Recently I'm interested in studying the dynamic behavior of global attractors and inertial manifolds of partial differential equations with respect to the perturbations of the domain and equation.

        Publications

        1. Structural stability for scalar reaction-diffusion equations (with L. Pires), Electronic Journal of Qualitative Theory of Diffential Equations, Vol. 1, No. 54 (2023), 1-12.
        2. Structural stability and rate of convergence of global attractors (with L. Pires), Nonlinear Analysis: Real World Applications, Vol. 74 (2023), 103947.
        3. Global attractors of generic reaction diffusion equations under Lipschitz Perturbations (with N. Nguyen and L. Pires), Journal of Mathematical Analysis and Applications, Vol. 528, No.2 (2023), 127534.
        4. Hyperbolicity, shadowing, and convergent operators (with C.A. Morales), Monatshefte fur Mathematik, Vol. 202, No. 3 (2023), 541-554.
        5. Topological stability of Chafee-Infante equations under Lipischitz perturbations of the domain and equation (with N. Nguyen), Journal of Mathematical Analysis and Applications, Vol. 517, No. 2 (2023), 126628.
        6. Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs (with C.A. Morales), Birkhauser Springer, 2022.
        7. Bowen-Walters expansiveness for sem​igroups of linear operators (with C.A. Morales), Ergodic Theory & Dynamical Systems (In press) doi:10.1017/etds.2022.20.
        8. Isometric vector fields from the Gromov–Hausdorff viewpoint (with C.A. Morales), Journal of Geometry 112 (2021), no 3, Paper No. 42, 11pp.
        9. Gromov-Hausdorff stability of inertial manifolds under perturbations of the domain and equations (with N. Nguyen), Journal of Mathematical Analysis and Applications, Vol. 494, No. 2 (2021), 124623.
        10. Gromov-Hausdorff stability of reaction diffusion equations with Neumann boundary conditions under perturbations of the domain, Journal of Mathematical Analysis and Applications, Vol. 496, No. 1 (2021), 124788.
        11. Spectral decomposition of flows with weak two-sided limit shadowing property (with N. Nguyen), Discrete and Continuous Dynamical Systems, Vol. 41, No. 9 (2021), 4375–4395.
        12. Gromov-Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations of the domain and equation (with Thanh Nguyen), Communications on Pure and Applied Analysis, Vol. 20, No.3 (2021), 1263–1296.
        13. Global attractors and exponential stability of partly dissipative reaction diffusion systems (with V.M. Toi), Applicable Analysis, Vol. 100. N0. 4 (2021), 735-751.
        14. On conormal and oblique derivative problem for elliptic equations with Dini mean oscillation coefficients (with H. Dong and S. Kim), Indiana University Mathematics Journal, Vol. 69, No. 2 (2020), 1815-1853.
        15. Gromov-Hausdorff stability of global attractors of reaction diffusion equations under perturbations of the domain (with N. Nguyen and V. M. Toi), Journal of Differential Equations, Vol. 269, No. 1 (2020), 125-147.
        16. Attractors for a class of delayed reaction diffusion equations with dynamic boundary conditions (with V. M. Toi), Discrete and Continuous Dynamical Systems B, Vol. 25, No. 8 (2020), 3135-3152.
        17. Attractors for nonclassical diffusion equations with dynamic boundary conditions (with V.M. Toi), Nonlinear Analysis, Vol. 195 (2020), 111737.
        18. On a class of Hamiltonian strongly degenerate elliptic systems with concave and convex nonlinearities (with T. Anh and Bui Kim M), Complex Variables and Elliptic Equations, Vol. 65, No. 4 (2020), 648-671.
        19. Boundary blow-up solutions to a class of degenerate elliptic equations, Analysis and Mathematical Physics, Vol. 9, No. 3 (2019), 1347-1361.
        20. On the classification of solutions to an elliptic equation involving the Grushin operator (with T. Anh and Bui Kim M), Complex Variables and Elliptic Equations, Vol. 63, No.5 (2018), 671-688.
        21. Dynamics of global attractor for a semilinear degenerate parabolic equation involving Grushin operators, Dynamic Systems and Applications, Vol. 27, No. 3 (2018), 457-474.

        Talks

        1. Hokkaido University, Sapporo, Japan, July 14, 2023.
        2. International Workshop on Dynamical Systems and Related Topics, VIASM, Hanoi, Jan 3-6, 2023.
        3. 2022 Conference of Honam Mathematical Society, Damyang, Korea, June 17-18, 2022.
        4. International Conference on Difference and Differential Equations and Applications 2019, Lisbon, Portugal, July 1-5, 2019.
        5. CMUP, University of Porto, Portugal, June 17-28, 2019.
        6. The 11th MSJ-SI 2018: The Role of Metrics in the Theory of Partial Differential Equations, Hokkaido University, Sapporo, Japan, July 2-13, 2018.
        7. 2018 Korean Mathematical Society Spring Meeting, April 20-22, 2018.

        Research Grant

          - Global Attractors and Inertial Manifolds of Infinite Dimensional Dynamical Systems
          - Project No: NRF-2023R1A2C1003119
          - Period: 01/Mar/2023 ~ 29/Feb/2028
          - Supported by National Research Foundation of Korea (NRF)