Proceedings of the Workshop on Energy Methods for Free Boundary Problems in Continuum Mechanics, held in Oviedo, Spain, March 21-23, 1994

Quasilinear parabolic equations with non-isotropic nonlinearities. Space and time localization.- On the boundary layer for dilatant fluids.- Minimal energy for a free ball on an elastic membrane.- Energy methods for higher order elliptic and parabolic problems.- The analysis of diffusion controlled reactions with non-equal diffusivities of the reactants.- The boundary-layer problems for some models of channel and filtration flows of a viscous compressible fluid.- Asymptotic stability for nonlinear parabolic systems.- Nonlocal symmetries in nonlinear heat equations.- Spatial decay estimates for cone-like shaped elastic solids.- Energy fluid motions stability for free boundary like problems in the exterior of convex starshaped domains.- Variational limit of compressible to incompressible fluid.- Stability thresholds for convection when the viscosity has a general form of temperature dependence.- Energy methods in Magnetohydrodynamics.

This volume contains the proceedings of the Workshop Energy Methods for Free Boundary Problems in Continuum Mechanics, held in Oviedo, Spain, from March 21 to March 23, 1994. It is well known that the conservation laws and the constitutive equations of Continuum Mechanics lead to complicated coupled systems of partial differential equations to which, as a rule, one fails to apply the techniques usually employed in the studies of scalar uncoupled equations such as, for instance, the maximum principle. The study of the qualitative behaviour of solutions of the systems re quires different techniques, among others, the so called, Energy Methods where the properties of some integral of a nonnegative function of one or several unknowns allow one to arrive at important conclusions on the envolved unknowns. This vol ume presents the state of the art in such a technique. A special attention is paid to the class of Free Boundary Problems. The organizers are pleased to thank the European Science Foundation (Pro gram on Mathematical treatment of free boundary problems), the DGICYT (Spain), the FICYT (Principado de Asturias, Spain) and the Universities of Oviedo and Complutense de Madrid for their generous financial support. Finally, we wish to thank Kluwer Academic Publishers for the facilities received for the publication of these Proceedings.