Existence Theorems in Elasticity

摘要: The subject to be developed in this article covers a very large field of existence theory for linear and nonlinear partial differential equations. Indeed, problems static elasticity, the propagation waves elastic media, thermodynamics continua require theorems elliptic, hyperbolic parabolic equations both nonlinear. Even if one restricts oneself there are several kinds considered. In we encounter second order systems, either with constant or variable coefficients (homogeneous non-homogeneous bodies), scalar (for instance St. Venant torsion membrane theory), fourth (equilibrium thin plates), eighth shells). Each case must considered boundary conditions, corresponding different physical situations. On other hand, every problem elasticity corresponds dynamical one, connected study vibrations system under consideration. Moreover, certain diffusion type. addition that, materials memory requires integro-differential equations, first by Volterra.