Reflections from artificial boundaries inhibit convergence of transient solutions to their steady limit. Far-field damping operators to suppress such reflections are presented for general first order hyperbolic systems, and particular reference is made to the compressible Euler equations. T h e damping operator has the following properties: (a) No reflections are generated due to the introducti...

We study the asymptotic behavior of compressible isentropic flow through porous medium when the initial mass is finite. The model system is the compressible Euler equation with frictional damping. As t → ∞, the density is conjectured to obey to the well-known porous medium equation and the momentum is expected to be formulated by Darcy’s law. In this paper, we prove that any L∞ weak entropy sol...

We study inviscid limits of invariant measures for the 2D Stochastic Navier-Stokes equations. As shown in [Kuk04] the noise scaling p ν is the only one which leads to non-trivial limiting measures, which are invariant for the 2D Euler equations. We show that any limiting measure μ0 is in fact supported on bounded vorticities. Relationships of μ0 to the long term dynamics of Euler in the L∞ with...

We study the asymptotic behavior of a compressible isentropic flow through a porous medium when the initial mass is finite. The model system is the compressible Euler equation with frictional damping. As t → ∞, the density is conjectured to obey the well-known porous medium equation and the momentum is expected to be formulated by Darcy’s law. In this paper, we give a definite answer to this co...

The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These modifications can obscure the effect of physical dissipation in the closed-loop. For example, generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In th...

This paper gives a detailed analysis of the physics of simple pendulum and the equations governing the motion and velocity. The pendulum works in three modes: simple, damped and driving and driving only. The signatures are evaluated and simulated by the means of four different approaches: Euler method, Euler-Cromer method, 2 nd order Runge-kutta method and built-in ODE-23 matlab solver. The sim...

We consider a compressible fluid structure interaction model in 2D channel with simplified expression of the net force acting on appearing at boundary. Concerning we will damped Euler-Bernoulli beam located portion In present article establish an observability inequality for adjoint linearized problem under consideration which principle is equivalent null controllability system. As corollary de...

We study a stabilization problem of system coupled by wave and Euler–Bernoulli plate equation. Only one the two equations is directly damped. Under some assumptions on damping coupling terms, we prove that sufficiently smooth solutions decay logarithmically without any geometric conditions domain. The proofs these results rely interpolation inequalities for elliptic-parabolic estimate resolvent...