- A. Nachaoui (Nantes University, France )
- Title: Cauchy's ptoblem for the modified biharmonic equation: ill-posedness and iterative regularizing methods
- Abstract : The modified biharmonic equation arises naturally when a semi-implicit scheme is used for the discretization of the incompressible Navier–Stokes equations and the resolution of the resulting boundary value problem at each time step is done via the use of the pure stream-function formulation. This equation supplemented with Cauchy boundary conditions gives rise to an inverse Cauchy problem. We show that this problem has a unique solution which does not depend continuously on the given noisy data. We build an iterative regularizing method. We show its convergence and we illustrate its efficiency via several examples.