Exponential stability for the wave equation with weak nonmonotone damping.
Exponential stability of a flexible structure with history and thermal effect
In this paper we study the asymptotic behavior of a system composed of an integro-partial differential equation that models the longitudinal oscillation of a beam with a memory effect to which a thermal effect has been given by the Green-Naghdi model type III, being physically more accurate than the Fourier and Cattaneo models. To achieve this goal, we will use arguments from spectral theory, considering a suitable hypothesis of smoothness on the integro-partial differential equation.
Exponential stability of linear and almost periodic systems on Banach spaces.
Exponential stability of positive solutions to some nonlinear heat equations.
Extended dynamical systems.
Extended limiting absorption method and analicity of the S-matrix.
Extinction and decay estimates of solutions for a class of porous medium equations.
Extremal equilibria for parabolic non-linear reaction-diffusion equations
Failure of convergence of the Lax-Oleinik semi-group in the time periodic case
Familles de convexes invariantes et équations de diffusion-réaction
Pour localiser la solution d’un système de diffusion-réaction, il suffit de construire une famille de convexes , invariante par rapport au champ de vecteurs associé à ce système; la solution est alors incluse dans à l’instant dès qu’elle est contenue dans à l’instant zéro. Les fonctions d’appui associées à de telles familles de convexes sont solutions d’un système différentiel, mais celui-ci peut également engendrer des familles non invariantes.
“Farfield” behavior of solutions to partial differential equations : asymptotic expansions and maximal rates of decay along a ray
Feedback stabilization of Navier–Stokes equations
One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a control problem associated with the linearized equation.
Feedback stabilization of Navier–Stokes equations
One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a LQ control problem associated with the linearized equation.
Feedback stabilization of semilinear heat equations.
Finite dimensional behavior for weakly damped driven Schrödinger equations
Finite fractal dimension of pullback attractors and application to non-autonomous reaction diffusion equations.
Finite-dimensionality of 2-D micropolar fluid flow with periodic boundary conditions
This paper is devoted to proving the finite-dimensionality of a two-dimensional micropolar fluid flow with periodic boundary conditions. We define the notions of determining modes and nodes and estimate their number. We check how the distribution of the forces and moments through modes influences the estimate of the number of determining modes. We also estimate the dimension of the global attractor. Finally, we compare our results with analogous results for the Navier-Stokes equation.
Finite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation
We address the problem of the existence of finite energy solitary waves for nonlinear Klein-Gordon or Schrödinger type equations in , , where . Under natural conditions on the nonlinearity , we prove the existence of in any dimension . Our result complements earlier works of Bartsch and Willem and Lorca-Ubilla where solutions invariant under the action of are constructed. In contrast, the solutions we construct are invariant under the action of where denotes the dihedral group...
First moments of energy and convergence to equilibrium.
Flutter panel equation in non cylindrical domain.