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.
This work is regarding solving 1-d wave equation using RPS semi-discretization method and analysis corresponding dispersion relation.
Various discrete adjoint methodologies are discussed for the inverse design of linear transport equations in 2 space dimensions
Tracking control of 1D scalar conservation laws in the presence of shocks