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.
Standing waves for nonlinear Schrödinger equations with singular potentials
Stark hamiltonians with periodic potentials
Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions.
Stationary solutions for the Cahn-Hilliard equation
Steady plane flow of viscoelastic fluid past an obstacle
We consider the steady plane flow of certain classes of viscoelastic fluids in exterior domains with a non-zero velocity prescribed at infinity. We study existence as well as asymptotic behaviour of solutions near infinity and show that for sufficiently small data the solution decays near infinity as fast as the fundamental solution to the Oseen problem.
Stochastic homogenization of a class of monotone eigenvalue problems
Stochastic homogenization (with multiple fine scales) is studied for a class of nonlinear monotone eigenvalue problems. More specifically, we are interested in the asymptotic behaviour of a sequence of realizations of the form It is shown, under certain structure assumptions on the random map , that the sequence of th eigenpairs converges to the th eigenpair of the homogenized eigenvalue problem For the case of -Laplacian type maps we characterize explicitly.
Strong asymptotic stability for n-dimensional thermoelasticity systems
We use a new approach to prove the strong asymptotic stability for n-dimensional thermoelasticity systems. Unlike the earlier works, our method can be applied in the case of feedbacks with no growth assumption at the origin, and when LaSalle's invariance principle cannot be applied due to the lack of compactness.
Strong convergence towards homogeneous cooling states for dissipative Maxwell models
Strong global attractor for a quasilinear nonlocal wave equation on .
Strong Lp-Solutions of the Navier-Stokes Equation in Rm, with Applications to Weak Solutions.
Structural stability for Brinkman-Forchheimer equations.
Subcritical approximation of the Sobolev quotient and a related concentration result
Sublinear elliptic equations in Rn.
Sul comportamento asintotico della soluzione di un problema di radiazione
Super and subsolutions for elliptic equations on all of .
Supersolutions and stabilization of the solutions of the equation∂u/∂t - div(|∇p|p-2 ∇u) = h(x,u), Part II.
In this paper we consider a nonlinear parabolic equation of the following type:(P) ∂u/∂t - div(|∇p|p-2 ∇u) = h(x,u)with Dirichlet boundary conditions and initial data in the case when 1 < p < 2.We construct supersolutions of (P), and by use of them, we prove that for tn → +∞, the solution of (P) converges to some solution of the elliptic equation associated with (P).