Variational formulation of steady flow in a hopper (Q1261749)

The author considers the flow of grandular material in a hopper on the assumption that the material is rigid-perfectly plastic. He formulates two variational problems, one referring to stress, and the other to strain and shows that they are dual under the Legendre transformation. The appropriate function spaces are discussed, and existence conditions are developed. Explicit solutions are developed for some problems and a discussion is given of an ill-posed free boundary problem which involves a conjecture in number theory.