DUNY_Zigic

We solve a family of variational PDE optimization problems numerically with a state-of-the-art adjoint-based Riemannian gradient method. We search for evidence of extreme and potentially singular behavior by systematically examining how relevant physical quantities scales with respect to a few fixed parameters. Our current focus is to formulate conjectures about bounds on the energy growth and the structure of extreme transient states in solutions to the 2D Kuramoto-Sivashinsky equation.