Maximal Regularity for Flexible Structural Systems in Lebesgue Spaces

Abstract

We study abstract equations of the form lambda u'''(t) + u"(t) = c(2) Au(t) + c(2)mu Au'(t) + f (t), 0 < lambda < mu which is motivated by the study of vibrations of flexible structures possessing internal material damping. We introduce the notion of (alpha;beta;gamma)-regularized families, which is a particular case of (a; k)-regularized families, and characterize maximal regularity in L-p-spaces based on the technique of Fourier multipliers. Finally, an application with the Dirichlet-Laplacian in a bounded smooth domain is given.