ENERGY DECAY OF ELECTROMAGNETIC SYSTEMS WITH MEMORY

We consider a linear evolution problem with memory arising in the theory of hereditary electromagnetism. Under general assumptions on the memory kernel, all single trajectories are proved to decay to zero, but the decay rate is not uniform in dependence of the initial data, so that the system is not exponentially stable. Nonetheless, if the kernel is rapidly fading and close to the Dirac mass at zero, then the solutions are close to exponentially stable trajectories.

A general asymptotic dynamic model for Lipschitzian elastic curved rods

We study the asymptotic behaviour of solutions to the linear evolution problem for clamped curved rods with the small thicknessεunder minimal regularity assumptions on the geometry. In addition, nonconstant density of the curved rods is considered.