Analyticity and Gevrey class regularity for a strongly damped wave equation with hyperbolic dynamic boundary conditions


We consider a linear system of PDEs of the form (Formula Presented) on a bounded domain Ω with boundary Γ=Γ 1∪Γ 0. We show that the system generates a strongly continuous semigroup T(t) which is analytic for α>0 and of Gevrey class for α=0. In both cases the flow exhibits a regularizing effect on the data. In particular, we prove quantitative time-smoothing estimates of the form ∥(d/dt)T(t)∥≲{pipe}t{pipe}-1 for α>0, ∥(d/dt)T(t)∥≲{pipe}t{pipe}-2 for α=0. Moreover, when α=0 we prove a novel result which shows that these estimates hold under relatively bounded perturbations up to 1/2 power of the generator. © 2013 Springer Science+Business Media New York.

Publication Title

Semigroup Forum