A chain rule in \(L^{1}\left({\operatorname*{div};\Omega}\right)\) and its applications to lower semicontinuity
A chain rule in the space \(L^{1}\left(\operatorname*{div};\Omega\right) \) is obtained under weak regularity conditions. This chain rule has important applications in the study of lower semicontinuity problems for general functionals of the form \(\int_{\Omega}f(x,u,\nabla u) dx\) with respect to strong convergence in \(L^{1}\left(\Omega\right) \) . Classical results of Serrin and of De Giorgi, Buttazzo and Dal Maso are extended and generalized.
As part of the LANL/VNIIEF collaboration a high velocity cylindrical liner driven Hugoniot experiment is being designed to be driven by a VNIEF Disk Explosive Magnetic (flux compression) Generator (DEMG). Several variations in drive current and liner thickness have been proposed. This presentation will describe the LANL 1D and 2D simulations used to evaluate those designs. The presentation will also propose an analysis technique to assess a high current drive systems ability to stably and optimally drive a cylindrical aluminum liner for this type of experiment.