Maximal Regularity for Flexible Structural Systems in Lebesgue Spaces

摘要

We study abstract equations of the form λu~(''')(t) + u~('')(t) = c~2Au(t) + c~2μAu~'(t)+f(t), 0 < λ < μ which is motivated by the study of vibrations of flexible structures 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 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.