On boundary exact controllability of one‐dimensional wave equations with weak and strong interior degeneration

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 boundary controllability of coupled hyperbolic equations

We study the exact boundary controllability of two coupled one dimensional wave equations with a control acting only in one equation. The problem is transformed into a moment problem. This framework has been used in control theory of distributed parameter systems since the classical works of A.G. Butkovsky, H.O. Fattorini and D.L. Russell in the late 1960s to the early 1970s. We use recent resu...

Feedback boundary stabilization of wave equations with interior delay

In this paper we consider a boundary stabilization problem for the wave equation with interior delay. We prove an exponential stability result under some Lions geometric condition. The proof of the main result is based on an identity with multipliers that allows to obtain a uniform decay estimate for a suitable Lyapunov functional. Mathematics Subject Classification (2000): 35B05, 93D15, 93D20

Local Exact Boundary Controllability of 3d Navier–stokes Equations

We consider the Navier–Stokes system in a bounded domain with a smooth boundary. Given a time-dependent solution and an arbitrary open subset of the boundary, we prove the existence of a boundary control, supported in the given subset, that drives the system to the given solution in finite time.

Exact controllability of wave equations in Rn coupled in parallel