We aim at developing a theory allowing the inverse design in the absence of **backward uniqueness** to be addressed both for linear and nonlinear problems. We shall take advantage of the fact that initial data recovered by backward **weak but not entropic solutions** can lead to the desired target by the forward entropic flow. This leads to the interesting and non-standard question of building numerical schemes to approximate non-entropic weak solutions. This program will also be developed in the context of **Hamilton-Jacobi** equations where, among the wide class of weak solutions, the physical ones are characterized by the viscosity criterion.

#### Available tutorials:

#### Two Grids Filter Method for RPS Semi-Discretization

This work is regarding solving 1-d wave equation using RPS semi-discretization method and analysis corresponding dispersion relation.

#### 2D inverse design of linear transport equations on unstructured grids

Various discrete adjoint methodologies are discussed for the inverse design of linear transport equations in 2 space dimensions

#### Conservation laws in the presence of shocks

Tracking control of 1D scalar conservation laws in the presence of shocks