Maximal regularity for flexible structural systems in Lebesgue spaces (Q966335)

Summary: We study abstract equations of the form \(\lambda u'''(t)+u''(t)=c_2Au(t)+c_2\mu Au'(t)+f(t)\), \(0<\lambda<\mu\) 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.