In most problems, the ideal situation is having the asymptotic dynamics of one equation the same as the asymptotic dynamics of its discretization. Although, when we are studying the linear wave equation, we note that the spectrum of discretization and the spectrum of its continuous counterpart are far away from each other, no matter how fine the discretization is. This fact is restrictive in th...

Lattice dynamical systems arise in various application fields, for instance, in chemical reaction theory, material science, biology, laser systems, image processing and pattern recognition, and electrical engineering (cf. [6, 7, 13]). In each field, they have their own forms, but in some other cases, they appear as spatial discretizations of partial differential equations (PDEs). Recently, many...

We prove a lower semicontinuity result for free discontinuity energies with a quasiconvex volume term having non standard growth and a surface term.

We establish a general weak* lower semicontinuity result in the space BD(Ω) of functions of bounded deformation for functionals of the form

A system of boundary-controlled piezoelectric beam equations, accounting for the interactions between mechanical vibrations and fully-dynamic electromagnetic fields, is considered. Even though electrostatic quasi-static field approximations Maxwell’s equations are sufficient most models systems, where magnetic permeability completely discarded, PDE model considered here retains pronounced wave ...