Part 1. Three-dimensional theory 3 Outline 3 1.1. Notation, definitions, and some basic formulas 3 1.2. Equations of equilibrium 5 1.3. Constitutive equations of elastic materials 8 1.4. The equations of nonlinear and linearized three-dimensional elasticity 11 1.5. A fundamental lemma of J.L. Lions 13 1.6. Existence theory in linearized three-dimensional elasticity 14 1.7. Existence theory in n...

we study the exponential decay of global solution for an n-dimensional thermo-elasticity systemin a bounded domain of ℜn . by using the multiplier technique and constructing an energy functional welladapted to the system, the exponential decay is proved.

natural convection between vertical parallel plates occurs frequently in applications such as solar collectors and cooling of electronic instruments. the problem is a two dimensional developing buoyant flow. in this work, the two dimensional conservation equations are solved numerically for constant wall temperature and constant wall heat flux. the results for the local nusselt number at the du...

SUMMARY The computation of a few smallest eigenvalues of generalized algebraic eigenvalue problems is studied. The considered problems are obtained by discretizing self-adjoint second-order elliptic partial diierential eigenvalue problems in two-dimensional or three-dimensional domains. The standard Lanczos algorithm with the complete orthogonalization is used to compute some eigenvalues of the...