On the well-posedness of some mechanical variational problems

The paper aims to establish the existence and uniqueness of the Solution of some variational problems constituting the basis of finite element modellings encountered in mechanics and civil engineering. And indeed, by expanding to the approximate problems coming from the space discretization, such theoretical results contribute to strengthen the robustness of the modelling softwares and the quality of their numerical results. More particularly, three kinds of mixed variational problems involving rheological non-linearities are considered here: the evolution problems of incompressible continua (solids or fluids) subjected to quasistatic small transformations, the problems of hydromechanical coupling and those coming from quasistatic large transformations of continua. Copyright (c) 2005 John Wiley & Sons, Ltd.