A remark on parabolic equations.
Exponential decay and existence of almost periodic solutions for some linear forced differential equations.
Théorèmes de surjectivité pour une classe d'opérateurs dans les espaces de Hilbert
Remarks on weak stabilization of semilinear wave equations
If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble....
Non-Resonance for a Strongly Dissipative Wave Equation in Higher Dimensions.
Anti-periodic solutions of some nonlinear evolution equations.
The Very Fast Solution of a Special Second Order ODE with Exponentially Decaying Forcing and Applications
Let , , be arbitrary positive constants and let be such that for some , we have . Then all solutions of tend to 0 as well as as tends to infinity. Moreover there exists a unique solution of (E) such that for some constant we have for all . Finally all other solutions of (E) decay to 0 either like or like as tends to infinity.
Équations d'évolution non linéaires : solutions bornées et périodiques
Soit un sous-différentiel (non coercif) dans un espace de Hilbert. On étudie l’existence de solutions bornées ou périodiques pour l’équation Deux solutions périodiques éventuelles diffèrent d’une constante. Si est périodique et compact, toute trajectoire bornée est asymptote pour à une trajectoire périodique.
Positively homogeneous functions and the Łojasiewicz gradient inequality
It is quite natural to conjecture that a positively homogeneous function with degree d ≥ 2 on satisfies the Łojasiewicz gradient inequality with exponent θ = 1/d without any need for an analyticity assumption. We show that this property is true under some additional hypotheses, but not always, even for N = 2.
Large time behaviour of the solutions to some nonlinear evolution equations
Remarks on weak stabilization of semilinear wave equations
If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble. ...
Pointwise and spectral control of plate vibrations.
We consider the problem of controlling pointwise (by means of a time dependent Dirac measure supported by a given point) the motion of a vibrating plate Ω. Under general boundary conditions, including the special cases of simply supported or clamped plates, but of course excluding the cases where multiple eigenvalues exist for the biharmonic operator, we show the controlability of finite linear combinations of the eigenfunctions at any point of Ω where no eigenfunction vanishes at any time greater...
Oscillations of anharmonic Fourier series and the wave equation.
In this paper we have collected some partial results on the sign of u(t,x) where u is a (sufficiently regular) solution of ⎧ utt + (-1)m Δmu = 0 (t,x) ∈ R x Ω ⎨ ⎩ u|Γ = ... = Δm-1 u|Γ = 0 t ∈ R. These results rely on the study of a sign of almost periodic functions of a special form restricted...
Équations d'évolution avec non linéarité logarithmique
Un théorème de valeurs intermédiaires dans les espaces de Sobolev et applications
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