Stability and Controllability of Differential Equations

We consider a system with a suitable boundary condition, where is a bounded domain, is a uniformly elliptic operator of the second order whose coefficients are suitably regular for , is fixed, and a function satisfies Our inverse problems are determinations of g using overdetermining data or , where and . Our main res…

For the solution u ( p ) = u ( p )( x , t ) to ∂ t 2 u ( x , t )-Δ u ( x , t )- p ( x ) u ( x , t ) = 0 in Ω × (0, T ) and (∂ u /∂ν)| ∂Ω × (0, T ) = 0 with given u (·,0) and ∂ t u (·,0), we consider an inverse problem of determining p ( x ), x ∊Ω, from data u |ω × (0, T ) . Here Ω⊂ n , n = 1,2,3, is a bounded domain,…

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Let u(f) be the solution to a hyperbolic equation in a bounded domain Omega subset R ': u"(x, t) = Delta u(x,t) + sigma (t)f(x) (x in Omega, 0 < t < T) u(x,0) = 0 u'(x,0) = 0 (x in Omega) u(x,t) = 0 (x in partial Omega, 0 < t < T). We assume that sigma in C 1 [0,T] is a known function, sigma(0) not= 0, and f in L 2 (O…

We study the stability of a flexible beam that is clamped at one end and free at the other; a mass is also attached to the free end of the beam. To stabilize this system we apply a boundary control force at the free end of the beam. We prove that the closed-loop system is well-posed and is exponentially stable. We the…

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• MASAHİRO YAMAMOTO

The author considers a flexible structure modeled as a rigid body which rotates in inertial space; a light flexible beam is clamped to the rigid body at one end and free one is clamped at the other. It is assumed that the flexible beam performs only planar motion. The equations of motion are obtained by using free bod…

A flexible beam, clamped to a rigid base at one end and free at the other end is considered. To stabilize the beam vibrations, a dynamic boundary force control and a dynamic boundary torque control applied at the free end of the beam are proposed. It is proved that with the proposed controls, the beam vibrations decay…

In this note, we consider a vertical cable which is pinched at the upper end. A mass is attached at the lower end where a control force is also applied. We show that this hybrid system is uniformly stabilized by choosing a suitable control law for the control force depending on the velocity and angular velocity at the…

For the solution u ( p ) = u ( p )( t , x ) to ∂ t 2 u ( t , x ) − div ( p ( x )∇ u ( t , x )) = 0 in (0, T ) × Ω with given u | (0, T ) × ∂Ω , u (0, ·) and ∂ t u (0, ·), we consider an inverse problem concerning the determination of the coefficient p ( x ), x ∊ Ω from data u | (0, T ) × ω . Here Ω ⊂ n is a bounded do…

We show a global Lipschitz estimate in determining a source term in a hyperbolic equation from overdetermining data on the lateral boundary. The method is a combination of the uniqueness result by the Carleman estimate and the compactness - uniqueness argument, and is also widely applicable to the determination of sou…

No abstract yet.

• MASAHİRO YAMAMOTO