Stability of higher-level energy norms of strong solutions to a wave equation with localized nonlinear damping and a nonlinear source term
Stability of hydrodynamic model for semiconductor
In this paper we study the stability of transonic strong shock solutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construction of a pseudo-local symmetrizer and on the paradifferential calculus with parameters, which combines the work of Bony-Meyer and the introduction of a large parameter.
Stability of periodic stationary solutions of scalar conservation laws with space-periodic flux
This article investigates the long-time behaviour of parabolic scalar conservation laws of the type , where and the flux is periodic in . More specifically, we consider the case when the initial data is an disturbance of a stationary periodic solution. We show, under polynomial growth assumptions on the flux, that the difference between u and the stationary solution behaves in norm like a self-similar profile for large times. The proof uses a time and space change of variables which is...
Stability of solutions of differential-operator and operator-difference equations with respect to perturbation of operators
Stability of solutions to the Cauchy problem for a plane hyperbolic system with time-periodic coefficients.
Stability of strong detonation waves and rates of convergence.
Stability of the Lagrange-Galerkin method with non-exact integration
Stability of vibrations for some Kirchhoff equation with dissipation
In this paper we consider the boundary value problem of some nonlinear Kirchhoff-type equation with dissipation. We also estimate the total energy of the system over any time interval with a tolerance level . The amplitude of such vibrations is bounded subject to some restrictions on the uncertain disturbing force . After constructing suitable Lyapunov functional, uniform decay of solutions is established by means of an exponential energy decay estimate when the uncertain disturbances are insignificant....
Stabilization and control for the subcritical semilinear wave equation
Stabilization beyond the distributions.
Stabilization of a wave-wave system.
Stabilization of Galerkin approximations of transport equations by subgrid modeling
This paper presents a stabilization technique for approximating transport equations. The key idea consists in introducing an artificial diffusion based on a two-level decomposition of the approximation space. The technique is proved to have stability and convergence properties that are similar to that of the streamline diffusion method.
Stabilization of second order evolution equations with unbounded feedback with delay
We consider abstract second order evolution equations with unbounded feedback with delay. Existence results are obtained under some realistic assumptions. Sufficient and explicit conditions are derived that guarantee the exponential or polynomial stability. Some new examples that enter into our abstract framework are presented.
Stabilization of solutions of an exterior boundary value problem for some class of evolution systems
Stabilization of the Schrödinger equation.
Stabilization of the wave equation by on-off and positive-negative feedbacks
Motivated by several works on the stabilization of the oscillator by on-off feedbacks, we study the related problem for the one-dimensional wave equation, damped by an on-off feedback . We obtain results that are radically different from those known in the case of the oscillator. We consider periodic functions : typically is equal to on , equal to on and is -periodic. We study the boundary case and next the locally distributed case, and we give optimal results of stability. In both cases,...
Stabilization of the wave equation by on-off and positive-negative feedbacks
Motivated by several works on the stabilization of the oscillator by on-off feedbacks, we study the related problem for the one-dimensional wave equation, damped by an on-off feedback . We obtain results that are radically different from those known in the case of the oscillator. We consider periodic functions a: typically a is equal to 1 on (0,T), equal to 0 on (T, qT) and is qT-periodic. We study the boundary case and next the locally distributed case, and we give optimal results of stability....
Stabilization of the wave equation with unbounded feedback of finite range.
Stabilization of wave systems with input delay in the boundary control
In the present paper, we consider a wave system that is fixed at one end and a boundary control input possessing a partial time delay of weight is applied over the other end. Using a simple boundary velocity feedback law, we show that the closed loop system generates a C0 group of linear operators. After a spectral analysis, we show that the closed loop system is a Riesz one, that is, there is a sequence of eigenvectors and generalized eigenvectors that forms a Riesz basis for the state Hilbert...
Stable upwind schemes for the magnetic induction equation
We consider the magnetic induction equation for the evolution of a magnetic field in a plasma where the velocity is given. The aim is to design a numerical scheme which also handles the divergence constraint in a suitable manner. We design and analyze an upwind scheme based on the symmetrized version of the equations in the non-conservative form. The scheme is shown to converge to a weak solution of the equations. Furthermore, the discrete divergence produced by the scheme is shown to be...