After modeling, the resulting mathematical problems are of a non-convex variational type. Additional material Click on thumbnails. Before this work, existing were essentially restricted to axisymmetric flows. Our original approach has already led to several significant results. A different, but connected, project consists of numerical studies related to the concept of viscosity solutions for general first order nonlinear PDEs.
Many applications call, however, for the use of vectorial equations.
We use systems of Hamilton-Jacobi equations as a way to formulate various problems from Solid Mechanics, a fundamentally new approach. Our numerical investigations take place in this context. Some older results, mostly about the Stefan problem and related questions.