Well Posedness for a Class of Flexible Structure in Hölder Spaces
Claudio Cuevas, Carlos Lizama · Mathematical Problems in Engineering · 2009
We characterize well‐posedness in Hölder spaces for an abstract version of the equation (∗) u′′ + λu′′′ = c2(Δu + μΔu′) + f which model the vibrations of flexible structures possessing internal material damping and external force f. As a consequence, we show that in case of the Laplacian with Dirichlet boundary conditions, equation (∗) is always well‐posed provided 0 < λ < μ.