36 research outputs found
Thermal Effects in a Two-Dimensional Hybrid Elastic Structure
AbstractIn this paper we consider a two-dimensional hybrid thermo-elastic structure consisting of a thermo-elastic plate which has a beam attached to its free end. We show that the initial-boundary-value problem for the interactive system of partial differential equations which take account of the mechanical strains/stresses and the thermal stresses in the plate and the beam, can be associated with a uniformly bounded evolution operator. It turns out that the interplay of parabolic dynamics due to the thermal effects in the hybrid structure and the hyperbolic dynamics associated with the elasticity of the structure yields analyticity for the entire system. This result yields solvability for the problem under optimal initial freedom of the displacement, velocity, and temperature in the plate and the beam, while uniform stability is readily available
Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions
In this paper we consider a multi-dimensional wave equation with dynamic
boundary conditions, related to the Kelvin-Voigt damping. Global existence and
asymptotic stability of solutions starting in a stable set are proved. Blow up
for solutions of the problem with linear dynamic boundary conditions with
initial data in the unstable set is also obtained
A global attractor for a fluid--plate interaction model accounting only for longitudinal deformations of the plate
We study asymptotic dynamics of a coupled system consisting of linearized 3D
Navier--Stokes equations in a bounded domain and the classical (nonlinear)
elastic plate equation for in-plane motions on a flexible flat part of the
boundary. The main peculiarity of the model is the assumption that the
transversal displacements of the plate are negligible relative to in-plane
displacements. This kind of models arises in the study of blood flows in large
arteries. Our main result states the existence of a compact global attractor of
finite dimension. We also show that the corresponding linearized system
generates exponentially stable -semigroup. We do not assume any kind of
mechanical damping in the plate component. Thus our results means that
dissipation of the energy in the fluid due to viscosity is sufficient to
stabilize the system.Comment: 18 page
Heat equation with dynamical boundary conditions of reactive-diffusive type
This paper deals with the heat equation posed in a bounded regular domain
coupled with a dynamical boundary condition of reactive-diffusive type,
involving the Laplace-Beltrami operator. We prove well-posedness of the problem
together with regularity of the solutions.Comment: 18 page