Optimization problems for 2-d conservation laws in presence of shocks.

Optimization problems for 2-d conservation laws in presence of shocks.

The objective of this talk is to outline a number of dificulties when approximating numerically optimization problems for conservation laws in higher dimensions. In particular, the gradient calculus of the cost functional and its numerical approximation to implement gradient type methods is discussed. In presence of shocks, this gradient cannot be computed in a classical way and shock displacements must be included in the calculus.

The one-dimensional case has been treated recently. We focus in the 2-d case where discontinuities in shock wavesare located in curves and the numerical treatment requires new developments.