Exact controllability for a degenerate and singular wave equation with moving boundary

Exact Controllability for a Semilinear Wave Equation with Both Interior and Boundary Controls

The purpose of this paper is to prove the existence of the exact controllability of a semilinear wave equation with both interior and boundary controls. Let Ω be a bounded open subset of Rn with a smooth boundary, let f (y) be an accretive mapping of L2(0,T ;H−1(Ω)) into L2(0,T ;H 0 (Ω)) with respect to a duality mapping J ,D( f ) = L2(0,T ;L2(Ω)) and having at most a linear growth in y. Consid...

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...

Boundary 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...

Geometrical Aspects of Exact Boundary Controllability for the Wave Equation a Numerical Study

This essentially numerical study sets out to investigate vari ous geometrical properties of exact boundary controllability of the wave equation when the control is applied on a part of the boundary Re lationships between the geometry of the domain the geometry of the controlled boundary the time needed to control and the energy of the control are dealt with A new norm of the control and an ener...

Exact Controllability for a Nonlinear Stochastic Wave Equation