VARIATIONAL FORMULATION FOR CONSTRAINED QUASILINEAR VECTOR SYSTEMS.

A variational formulation for multi-dimensional initial- and/or boundary-value problems for a system of quasiliner conservation equations with a rotationality condition in a vector form with the aid of a vector Lagrange multiplier is given. The duality between the physical and 'phase' (or hodograph) spaces emerges, and the Lagrange multiplier turns out to be the vector potential for the conserved field, and hence of some interest in itself. Application is given to a family of transonic flows in the physical and hodograph planes, and to a problem in nonlinear sound propagation.