Kinetic and hydrodynamic equations for granular media
In this lecture i present some open mathematical problems concerning some PDE arising in the study of one-dimensional models for granular media.
--Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity
We prove the --time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the --time decay estimates.
La scelta delle interazioni inerziali nei continui con microstruttura
Dedicando speciale attenzione all’esempio significativo dei cristalli liquidi di Ericksen [6], viene presentato un apparato assiomatico che consente di dedurre rappresentazioni coerenti delle interazioni d’inerzia e dell’energia cinetica per continui con microstruttura.
Lamb's plane problem in a thermoelastic micropolar medium with stretch.
Lamb's plane problem in a thermo-visco-elastic micropolar medium with the effect of gravity.
Lavrentiev phenomenon in microstructure theory.
Le calcul des caractéristiques effectives pour des matériaux composites qui contiennent des nonhomogénéites attribuées d'une manière aléatoire. (Calculation of effective properties of composite materials with random inhomogeneities).
Least square method for solving contact problems with friction obeying the Coulomb law
The paper deals with numerical realization of contact problems with friction obeying the Coulomb law. The original problem is formulated as the fixed-point problem for a certain operator generated by the variational inequality. This inequality is transformed to a system of variational nonlinear equations generating other operators, in a sense "close" to the above one. The fixed-point problem of these operators is solved by the least-square method in which equations and the corresponding quadratic...
Lectures on constitutive expressions
Libere vibrazioni di solidi termoelastici incomprimibili
Line Fields with Branch Defects.
Linear approximation in Continuum Mechanics
Some critical remarks are made about the theory of Linear Elasticity, questioning on its validity in general. An alternative linear approximation of the exact theory is proposed.
Material constraints in continuum mechanics
Si dimostra che ci sono valide ragioni per considerare la teoria standard dei vincoli interni, nella meccanica dei continui, insufficientemente generale. In particolare, con l’unica eccezione dell’iperelasticità, l’extra-stress dovrebbe dipendere anche dai moltiplicatori di Lagrange, cioè, dallo stress che non effettua lavoro (virtuale).
Mathematical approach to the relaxation phenomena.
Mathematical models of phenomenological piezoelectricity
Mathematical study of an evolution problem describing the thermomechanical process in shape memory alloys
In this paper we prove existence, uniqueness, and continuous dependence for a one-dimensional time-dependent problem related to a thermo-mechanical model of structural phase transitions in solids. This model assumes the free energy depending on temperature, macroscopic deformation and also on the proportions of the phases. Here we neglect regularizing terms in the momentum balance equation and in the constitutive laws for the phase proportions.
Mechanical design problems with unilateral contact
Mechanics Of Growing Materials With Memory
Mechanics of growing materials with memory.
Mesoscopic description of boundary effects in nanoscale heat transport
We review some of the most important phenomena due to the phonon-wall collisions in nonlocal heat transport in nanosystems, and show how they may be described through certain slip boundary conditions in phonon hydrodynamics. Heat conduction in nanowires of different cross sections and in thin layers is analyzed, and the dependence of the thermal conductivity on the geometry, as well as on the roughness is pointed out. We also analyze the effects of the roughness of the surface of the pores on the...