A Conservative Eulerian Formulation of the Equations for Elastic Flow

The partial differential equations describing the deformation of an elastic body support a rich variety of waves (shock, shear, and torsion) as solutions. A scientific understanding of these wave solutions requires a mathematical analysis of the structure of the governing equations, combined with numerical computation of the solutions. When studying quasi-linear hyperbolic partial differential equations, whose solutions typically develop discontinuities, one must begin by writing the equations as a system of conservation laws. Assuming that there are n independent conserved quantities, the solution is specified by a vector U(X, t) that lies in an n-dimensional state space. The dynamical equations for u take the form ;+v *j(u)=0 (1.1)