Maximal Regularity for Flexible Structural Systems in Lebesgue Spaces

Abstract EN

We study abstract equations of the form λu′′′(t)+u′′(t)=c2Au(t)+c2μAu′(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 Lp-spaces based on the technique of Fourier multipliers.

Finally, an application with the Dirichlet-Laplacian in a bounded smooth domain is given.