On a generalized system of equations in continuum mechanics (Q1062807)

A system of equations which generalizes the equations of isotropic elasticity and the Stokes equations of hydrodynamics is considered. Using a matrix inversion technique, Galerkin-type representations are obtained. The fundamental singular solutions are then derived and via reciprocal relationship the integral representations by potentials are obtained. The advantage of the proposed method is that the Dirichlet boundary-value problem of elasticity and the Stokes equations of hydrodynamics can be treated simultaneously.