Mathematical Problems in Elasticity

Abstract

In this volume, five papers are collected that give a good sample of the problems and the results characterizing some recent trends and advances in this theory. Some of them are devoted to the improvement of a general abstract knowledge of the behaviour of elastic bodies, while the others mainly deal with more applicative topics. The first paper entitled Collected Results on Finite Amplitude Plane Waves in Deformed Mooney-Rivlin Materials by Ph. Boulanger and M. Hayes gives a complete and systematic exposition of a body of selected results concerning the propagation of finite-amplitude plane waves in a deformed Mooney-Rivlin material. C.O. Horgan's paper entitled Decay Estimates for Boundary Value Problems in Linear and Nonlinear Continuum Mechanics provides a review of recent results concerning the decay at large spatial distance of solutions to (systems of) elliptic partial differential equations. In the third paper On the Traction Problem in Incompressible Linear for Unbounded Domains by R. Russo and G. Starita, the well-posedness (existence, uniqueness and continuous dependence of solutions upon the data) of the traction problem in incompressible linear elasticity for three-dimensional exterior domains is proved in the class of solutions with finite energy. The paper contributed by T. Valent An Abstract Perturbation Problem with Symmetries Suggested by Live Boundary Problems in Elasticity deals with an abstract formulation for boundary problems with symmetries, and with a study of a general perturbation problem with symmetries. The fifth paper Maximum Principles in Classical Elasticity by L.T. Wheeler, owes its interest to a wide discussion of the applications of maximum principles for scalar-valued functions to classical theory of elasticity.