DIFFERENTIAL & INTEGRAL EQUATIONS SEMINAR
Faculty of Mathematics and Information Technology, Hanoi National University of Education

Chairperson: Prof. Dr.Sc. Nguyen Manh Hung
Core members:

1. Dr. Tran Thi Loan 2. Dr. Le Van Hien
3. Dr. Pham Trieu Duong 4. Dr. Nguyen Thi Kim Son
5. Dr. Tran Dinh Ke (Secretary) 6. PhD student Nguyen Thi Lien
7. Dr. Nguyen Duc Huy 8. PhD student Phung Kim Chuc
9. Dr. Cung The Anh 10. PhD student Bui Trong Kim
11. Dr. Nguyen Thanh Anh 12. Bachelor Nguyen Thi Van Anh

Time: 9:00am Wednesday, Weekly.
Venue: Room 116, Blk C, Hanoi National University of Education.
About the Seminar series: The Seminar series “Partial Differential equations”, chaired by Professor Doctor of Science Nguyen Manh Hung, was held every Wednesday, 9AM, since 2000. Due to the development of the department (Department of Analysis Mathematics, Faculty of Mathematics and Information Technology, HNUE), the Seminar series has been renamed and known as "Differential & Integral Equations" since 2009. The Seminar series is the playground for the department's members, PhD students, Master students, and Bachelor students within and outside of the University. It is also the place to welcome international renowned professors to come to work and exchange research experience, and the place for international education organization to contact for reviewing. The Seminar series contributed significantly to the department's research and PhD/Master training. Especially, it formed a research group of rapid growth, with efficient coordination between members and expansion of collaboration with national and international experts. In the last 5 years (2006-2011), the Seminar series' members have published more than 70 research papers on international high-profile journals. Currently, the Seminar series' members are directing 02 national-level project sponsored by NAFOSTED, 01 Ministry-level project and 02 University-level projects.

The main research topics:

  1. Theory of boundary value problems for partial differential equations and systems in nonsmooth domains: We study initial-boundary value problems for nonstationary (hyperbolic, parabolic, Schrodinger, etc.) equations and systems in nonsmooth domains (with conical points, with edges, polyhedral, etc.) in which the solvability, the regularity and the asymptotic behavior of the solutions near singular points are investigated. Several papers in this topic have been published in recent years. It remains open problems attracting our attention to study.
  2. Asymptotic Behavior of Solutions of Differential Equations: We study the long-time behavior of solutions as t goes to infinity (including stability, existence and properties of attractors) of infinite-dimensional dynamical systems generated by nonlinear dissipative partial differential equations or differential equations with delay. We have established many results on the existence and properties of attractors for some classes of semilinear quasilinear degenerate parabolic equations, and on the stability of solutions of many ordinary differential equations with delay and some retarded parabolic equations. The aim of current research is to study the long-time behavior of solutions of equations arising in fluid mechanics (such as the Navier-Stokes equations and its generalizations, the KdV equation and some related equations), and of partial functional differential equations.
  3. Mathematical Control: We study control problems (exact controllability, null controllability, approximate controllability, optimal controllability) for both ordinary and partial differential equations, and for evolution inclusions. This is a new research direction of the Division. The aim of current research is to study the above control problems for degenerate parabolic equations, partial differential equations with singular potentials of Hardy type and some evolution inclusions.
  4. Differential Inclusions: We study the existence of solutions, controllability, optimization, and asymptotic behavior of solution for differential inclusions. We have obtained some recent results in this direction.
  5. Nonlinear Partial Differential Equations: We study the existence, regularity, numerical approximations, and long-time behavior of some classes of nonlinear partial equations, especially semilinear elliptic equations and equations in fluid mechanics, for full models (Euler, Navier-Stokes equations and related equations) as well as asymptotic models (KdV, Boussinesq, etc.).


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