NORMAL HYPERBOLICITY OF CENTER MANIFOLDS AND SAINTVENANT PRINCIPLE

The concept of normal hyperbolicity of center manifolds is generalized to infinite-dimensional differential equations, in particular, to elliptic problems in cylindrical domains. It is shown that all solutions u staying close to the center manifold for t ∈ (-l,l) satisfy an estimate of the form {Mathematical expression} where C and α are independent of l, and ũ is a solution on the center manifold. These results are applied to Saint-Venant's principle for the static deformation of nonlinearly elastic prismatic bodies. The use of the center manifold permits the effective treatment of the general case of non-zero resultant forces and moments acting on each cross-section. © 1990 Springer-Verlag.