858 research outputs found
Boundary Stabilization of Quasilinear Maxwell Equations
We investigate an initial-boundary value problem for a quasilinear
nonhomogeneous, anisotropic Maxwell system subject to an absorbing boundary
condition of Silver & M\"uller type in a smooth, bounded, strictly star-shaped
domain of . Imposing usual smallness assumptions in addition to
standard regularity and compatibility conditions, a nonlinear stabilizability
inequality is obtained by showing nonlinear dissipativity and
observability-like estimates enhanced by an intricate regularity analysis. With
the stabilizability inequality at hand, the classic nonlinear barrier method is
employed to prove that small initial data admit unique classical solutions that
exist globally and decay to zero at an exponential rate. Our approach is based
on a recently established local well-posedness theory in a class of
-valued functions.Comment: 22 page
Boundary stabilization and control of wave equations by means of a general multiplier method
We describe a general multiplier method to obtain boundary stabilization of
the wave equation by means of a (linear or quasi-linear) Neumann feedback. This
also enables us to get Dirichlet boundary control of the wave equation. This
method leads to new geometrical cases concerning the "active" part of the
boundary where the feedback (or control) is applied. Due to mixed boundary
conditions, the Neumann feedback case generate singularities. Under a simple
geometrical condition concerning the orientation of the boundary, we obtain a
stabilization result in linear or quasi-linear cases
Boundary feedback stabilization of a flexible wing model under unsteady aerodynamic loads
This paper addresses the boundary stabilization of a flexible wing model,
both in bending and twisting displacements, under unsteady aerodynamic loads,
and in presence of a store. The wing dynamics is captured by a distributed
parameter system as a coupled Euler-Bernoulli and Timoshenko beam model. The
problem is tackled in the framework of semigroup theory, and a Lyapunov-based
stability analysis is carried out to assess that the system energy, as well as
the bending and twisting displacements, decay exponentially to zero. The
effectiveness of the proposed boundary control scheme is evaluated based on
simulations.Comment: Published in Automatica as a brief pape
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