Identification of nonlinear coefficient in a transport equation.
Ill-posedness of the Cauchy problem for totally degenerate system of conservation laws.
Implicit difference method for nonlinear first order partial differential equations.
Increasing smoothness of solutions to a hyperbolic system on the plane with delay in the boundary conditions.
Indirect stabilization of locally coupled wave-type systems
We study in an abstract setting the indirect stabilization of systems of two wave-like equations coupled by a localized zero order term. Only one of the two equations is directly damped. The main novelty in this paper is that the coupling operator is not assumed to be coercive in the underlying space. We show that the energy of smooth solutions of these systems decays polynomially at infinity, whereas it is known that exponential stability does not...
Indirect stabilization of locally coupled wave-type systems
We study in an abstract setting the indirect stabilization of systems of two wave-like equations coupled by a localized zero order term. Only one of the two equations is directly damped. The main novelty in this paper is that the coupling operator is not assumed to be coercive in the underlying space. We show that the energy of smooth solutions of these systems decays polynomially at infinity, whereas it is known that exponential stability does not...
Inégalité d'observabilité du type logarithmique et estimation de la fonction de coût des solutions des équations hyperboliques
Dans ce travail, nous donnons une estimation logarithmique des données de la solution u, d'un problème hyperbolique avec condition aux limites de type Neumann, par la trace de u restreinte à un ouvert du bord, pendant un temps suffisamment grand qui nous permet d'estimer la fonction de coût de ce problème.
Inégalités de résolvante pour l’opérateur de Schrödinger avec potentiel multipolaire critique
On étudie un opérateur de la forme sur , où est un potentiel admettant plusieurs pôles en . Plus précisément, on démontre l’estimation de résolvante tronquée à hautes fréquences, classique dans les cas non-captifs, et qui implique l’effet régularisant standard pour l’équation de Schrödinger correspondante. La preuve est basée sur l’introduction d’une mesure de défaut micro-locale semi-classique. On démontre également, dans le même contexte, des inégalités de Strichartz pour l’équation de Schrödinger....
Inégalités de Strichartz et équations d’ondes quasilinéaires
Dans ce texte, notre but est de résoudre des équations d’ondes quasilinéaires pour des données initiales moins régulières que ce qu’impose les méthodes d’énergie. Ceci impose de démontrer des estimées de type Strichartz pour des opérateurs d’ondes à coefficients seulement lipschitziens.
Inégalités de Strichartz généralisées pour l'équation des ondes
Inégalités pour un problème de Goursat
Inequalities for spherically symmetric solutions of the wave equation.
Inertial manifolds and stabilization of nonlinear beam equations with Balakrishnan-Taylor damping.
Inertial manifolds for retarded second order in time evolution equations in admissible spaces
Using the Lyapunov-Perron method, we prove the existence of an inertial manifold for the process associated to a class of non-autonomous semilinear hyperbolic equations with finite delay, where the linear principal part is positive definite with a discrete spectrum having a sufficiently large distance between some two successive spectral points, and the Lipschitz coefficient of the nonlinear term may depend on time and belongs to some admissible function spaces.
Inertial manifolds of damped semilinear wave equations
Infinite systems of first order PFDEs with mixed conditions
We consider mixed problems for infinite systems of first order partial functional differential equations. An infinite number of deviating functions is permitted, and the delay of an argument may also depend on the spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral systems...
Infinitely many periodic solutions of nonlinear wave equations on .
Infinitely narrow soliton solutions to systems of conservation laws.
Influence of bottom topography on long water waves
We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom topography, one for small variations in amplitude, and one for strong variations. Starting from the Zakharov formulation of this problem, we rigorously compute the asymptotic expansion of the involved Dirichlet-Neumann operator. Then, following the global strategy...
Ingham type theorems and applications to control theory
Ingham [6] ha migliorato un risultato precedente di Wiener [23] sulle serie di Fourier non armoniche. Modificando la sua funzione di peso noi otteniamo risultati ottimali, migliorando precedenti teoremi di Kahane [9], Castro e Zuazua [3], Jaffard, Tucsnak e Zuazua [7] e di Ullrich [21]. Applichiamo poi questi risultati a problemi di osservabilità simultanea.