Asymptotics of Hamilton–Jacobi equations in the stationary ergodic case (ESR16) ***this position has been filled***

• Title : Asymptotics of Hamilton–Jacobi equations in the stationary ergodic case.
  
• Application deadline: May 15, 2011 or until the position is filled.
  
• Location:  Università Degli Studi di Roma - La Sapienza, Italy
• Secondment: INRIA, France
• Funding: 36 months
• Contact:Antonio Siconolfi
  
• Description of the subject:

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.

• Requirements:  MSc degree in mathematics or a related subject.
  

Applications including a full curriculum vitae, and the names and addresses of at least two referees should be sent to Contact.