Uniform analyticity and exponential decay of the semigroup associated with a thermoelastic plate equation with perturbed boundary conditions

作者：Tebou Louis^*

来源：Comptes Rendus Mathematique, 2013, 351(13-14): 539-544.

DOI：10.1016/j.crma.2013.07.014

In a bounded domain, we consider an Euler-Bernoulli-type thermoelastic plate equation with perturbed boundary conditions. The boundary conditions are such that when the perturbation parameter goes to infinity, we recover the hinged boundary conditions, while one recovers the clamped boundary conditions when the perturbation parameter goes to zero. Relying on resolvent estimates, we show that the underlying semigroup is uniformly, with respect to the perturbation parameter, analytic and exponentially stable. The main features of our proof are appropriate decompositions of the components of the system and the use of Lions' interpolation inequalities.

• 出版日期2013-7