Factor spaces and implications of Kirchhoff equations with clamped boundary conditions.
Failure of analytic hypoellipticity in a class of differential operators
For the hypoelliptic differential operators introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of and left open in the analysis, the operators also fail to be analytic hypoelliptic (except for ), in accordance with Treves’ conjecture. The proof is constructive, suitable for generalization, and relies on evaluating a family of eigenvalues of a non-self-adjoint operator.
Failure of convergence of the Lax-Oleinik semi-group in the time periodic case
Faisceaux maximaux de fonctions associées à un opérateur elliptique du second ordre
Soit le faisceau des sursolutions variationnelles d’un opérateur différentiel elliptique du second ordre à coefficients . Soit le faisceau des régularitées essentielles inférieures des éléments de . On démontre que est contenu dans un seul préfaisceau maximal de cônes convexes de fonctions s.c.i. vérifiant le principe du minimum sur une base d’ouverts suffisamment petits. On démontre que possède toutes les bonnes propriétés d’une théorie locale du potentiel.
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.
Fatou theorems for some nonlinear elliptic equations.
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.
Fibered microstructures for some nonlocal Dirichlet forms
Fine topology and quasilinear elliptic equations
It is shown that the -fine topology defined via a Wiener criterion is the coarsest topology making all supersolutions to the -Laplace equationcontinuous. Fine limits of quasiregular and BLD mappings are also studied.
Finite dimensional behavior for weakly damped driven Schrödinger equations
Finite dimensional dynamics for Kolmogorov-Petrovsky-Piskunov equation.
Finite dimensional global attractor for a class of doubly nonlinear parabolic equations
Our aim in this paper is to study the long time behavior of a class of doubly nonlinear parabolic equations. In particular, we prove the existence of the global attractor which has, in one and two space dimensions, finite fractal dimension.
Finite dimensional uniform attractors for the nonautonomous Camassa-Holm equations.
Finite fractal dimension of pullback attractors and application to non-autonomous reaction diffusion equations.
Finite speed of propagation for a non-local porous medium equation
This note is concerned with proving the finite speed of propagation for some non-local porous medium equation by adapting arguments developed by Caffarelli and Vázquez (2010).
Finite-dimensional Pullback Attractors for Non-autonomous Newton-Boussinesq Equations in Some Two-dimensional Unbounded Domains
We study the existence and long-time behavior of weak solutions to Newton-Boussinesq equations in two-dimensional domains satisfying the Poincaré inequality. We prove the existence of a unique minimal finite-dimensional pullback -attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms.
Finite-dimensional pullback attractors for parabolic equations with Hardy type potentials
Using the asymptotic a priori estimate method, we prove the existence of a pullback -attractor for a reaction-diffusion equation with an inverse-square potential in a bounded domain of (N ≥ 3), with the nonlinearity of polynomial type and a suitable exponential growth of the external force. Then under some additional conditions, we show that the pullback -attractor has a finite fractal dimension and is upper semicontinuous with respect to the parameter in the potential.
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.