Maximal Regularity for Flexible Structural Systems in Lebesgue Spaces
Claudio Fernández, Carlos Lizama, Verónica Poblete · Mathematical Problems in Engineering · 2010
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.