The Wave Equation with Dynamic Wentzell Boundary Condition in Polygonal and Polyhedral Domains: Observation and Exact Controllability
نویسنده
چکیده
We consider the problem of observation and control of a system of transmission waves. The system is governed by a three-dimensional (respectively two-dimensional) D’ Alembert wave equation in a bounded domain which comprises corners but which is not fissured. On the boundary we have inside an artificial dynamic Wentzell boundary condition coupled with the internal equation by the normal derivative. Let us start by giving a few motivations of interest in the study of observation, control, stabilization and inverse problems with artificial conditions: The condition at the boundary can be seen like a contribution of energy (kinetic energy and potential
منابع مشابه
Exact Controllability for a Wave Equation with Mixed Boundary Conditions in a Non-cylindrical Domain
In this article we study the exact controllability of a one-dimensional wave equation with mixed boundary conditions in a non-cylindrical domain. The fixed endpoint has a Dirichlet-type boundary condition, while the moving end has a Neumann-type condition. When the speed of the moving endpoint is less than the characteristic speed, the exact controllability of this equation is established by Hi...
متن کاملAn Exact Elastodynamic Solution for Func-tionally Graded Thick-Walled Cylinders Subjected to Dynamic Pressures
In the present paper, an exact solution for transient response of an infinitely long functionally graded thick-walled cylinder subjected to dynamic pressures at the boundary surfaces is presented for arbitrary initial conditions. The cylinder is assumed to have a plane-strain condition and the dynamic pressures are assumed to be imposed uniformly and axis...
متن کاملStress Waves in a Generalized Thermo Elastic Polygonal Plate of Inner and Outer Cross Sections
The stress wave propagation in a generalized thermoelastic polygonal plate of inner and outer cross sections is studied using the Fourier expansion collocation method. The wave equation of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermoelastic plate of polygonal shape, composed of homogeneous isotropic material. The freque...
متن کاملBoundary controllability for the quasilinear wave equation
We study the boundary exact controllability for the quasilinear wave equation in the higher-dimensional case. Our main tool is the geometric analysis. We derive the existence of long time solutions near an equilibrium, prove the locally exact controllability around the equilibrium under some checkable geometrical conditions. We then establish the globally exact controllability in such a way tha...
متن کاملLocal exact controllability of the 2D-Schrödinger-Poisson system
In this article, we investigate the exact controllability of the 2DSchrödinger-Poisson system, which couples a Schrödinger equation on a bounded domain of R with a Poisson equation for the electrical potential. The control acts on the system through a Neumann boundary condition on the potential, locally distributed on the boundary of the space domain. We prove several results, with or without n...
متن کامل