Fluid flow in macromolecular systems and related perturbation problems
We prove the existence and find necessary and sufficient conditions for the uniqueness of the time-periodic solution to the equations for an arbitrary (sufficiently smooth) periodic right-hand side , where denotes the Laplace operator with respect to , and is the Ishlinskii hysteresis operator. For this equation describes e.g. the vibrations of an elastic membrane in an elastico-plastic medium.
This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems of periodic...
This article is divided into two chapters. The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in the first chapter. Following a Fourier approach, we discuss some of the basic issues of the subject: main convergence theorem, Bloch approximation, estimates on second order derivatives, correctors for the medium, and so on. The second chapter is devoted to the discussion of some non-classical behaviour of vibration problems of periodic...
It is shown, in the context of the Thermomechanics of simple materials with memory, that frame indifference and, equivalently, rotation invariance are necessary consequences of the laws of classical Mechanics and the definition of the stress matrix and heat flux vector.
In connection with the determination of the free energy functional for the viscoelastic stress tensor, a viscoelastic material is considered as described by a material with internal variables. In this framework the free energy is uniquely determined. It proves to be the minimal one in the class of thermodynamically admissible free energies.