Nguyen Ngoc Quoc Thuong

Thuong is a Vietnamese PhD student recruited by La Sapienza University of Rome. He is working on Asymptotics of Hamilton–Jacobi equations in the stationary ergodic case and will be seconded to INRIA.

Thuong.jpgNguyen Ngoc Quoc Thuong  - University of Rome

  • Main host organisation: Università di Roma - La Sapienza, Italy
  • Supervisors: Antonio Siconolfi and Maurizio Falcone
  • Secondment organisation: INRIA, France
  • Nationality: Vietnamese
  • Fellowship duration: November 2011 - October 2014
  • Background: Thuong obtained a master's degree in Mathematics from Thai Nguyen University and Hanoi Institute of Mathematics, Vietnam in 2009. He also participated in the ICTP Postgraduate Diploma Programme in Mathematics at The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy from September 2010 to August 2011.
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SADCO research project: Asymptotics of Hamilton–Jacobi equations in the stationary ergodic case  
Our intention is to develop a basic asymptotic theory for Hamilton-Jacobi (HJ) equations, suitable for application to control problems and differential games, within an ergodic, stationary setting. So far, many important issues are still unresolved. For stationary ergodic convex Hamiltonians, it is not clear, for instance, if the associated cell problems admit approximate solutions as in the quasi–periodic case. The existence of such objects would make it possible to carry out an asymptotic analysis by means of Evans’ perturbed function method. So far, all known results on this subject are based upon the use of appropriate representation formulae for solutions. However, such representation formulae are very difficult to deal with when the Hamiltonian is nonconvex. For this reason, the nonconvex setting is more difficult to investigate. We shall focus attention on problems with positively homogeneous Hamiltonians. For such problems, we shall exploit the well-known geometric interpretation of solutions to the associated HJ equation, in terms of the level set evolution, with respect to an associated intrinsic distance; this property is a feature of the nonconvex, as well as the convex, case.



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