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

作者：Graber Philip Jameson^*; Lasiecka Irena

来源：Semigroup Forum, 2014, 88(2): 333-365.

DOI：10.1007/s00233-013-9534-3

• Gevrey's semigroups
• Analytic semigroups
• Wave equation with dynamic boundary conditions
• Pseudodifferential operators

We consider a linear system of PDEs of the form <Equation ID="Equ1"> <EquationNumber>1</EquationNumber> <MediaObject> </MediaObject> </Equation> on a bounded domain Omega with boundary I"=I" (1)a(a)I" (0). We show that the system generates a strongly continuous semigroup T(t) which is analytic for alpha > 0 and of Gevrey class for alpha=0. In both cases the flow exhibits a regularizing effect on the data. In particular, we prove quantitative time-smoothing estimates of the form ayen(d/dt)T(t)ayena parts per thousand(2)|t|(-1) for alpha > 0, ayen(d/dt)T(t)ayena parts per thousand(2)|t|(-2) for alpha=0. Moreover, when alpha=0 we prove a novel result which shows that these estimates hold under relatively bounded perturbations up to 1/2 power of the generator.

• 出版日期2014-4
• 单位INRIA