Verónica Poblete

Maximal Regularity for Flexible Structural Systems in Lebesgue Spaces

We study abstract equations of the form , which is motivated by the study of vibrations of flexible structures possessing internal material damping. We introduce the notion of -regularized families, which is a particular case of -regularized families, and characterize maximal regularity in -spaces based on the technique of Fourier multipliers. Finally, an application with the Dirichlet-Laplacian in a bounded smooth domain is given.

Regularity of solutions for a third order differential equation in Hilbert spaces

We study regularity of mild and strong solutions of an abstract mathematical model of a flexible space structure under appropriate initial conditions. We apply our results showing qualitative properties of the trajectories in the case of the negative Laplacian operator.