Maximal Regularity for Flexible Structural Systems in Lebesgue Spaces

摘要

We study abstract equations of the formλu′′′(t)+u′′(t)=c2Au(t)+c2μAu′(t)+f(t),0<λ<μwhich is motivated by the study of vibrations of flexiblestructures possessing internal material damping. We introduce the notion of(α;β;γ)-regularized families, which is a particular case of(a;k)-regularized families, and characterizemaximal regularity inLp-spaces based on the technique of Fourier multipliers. Finally, an application with the Dirichlet-Laplacian in a bounded smooth domain isgiven.