Abrupt and smooth separation of free boundaries in flow problems
Abschätzung nach unten für Lösungen nichtlinearer Differentialungleichungen
Absence de principe du maximum pour certaines équations paraboliques complexes
Le but de cette note est de montrer que le principe du maximum, même dans une version affaiblie, n’est pas vérifıé pour la classe des opérateurs paraboliques du type , où L est un opérateur différentiel elliptique d’ordre 2 sous forme divergence à coefficients complexes mesurables et bornés en dimension supérieure ou égale à 5. Le principe de démonstration repose sur un résultat abstrait de la théorie des semi-groupes permettant d’utiliser le contre-exemple présenté dans [MNP] à la régularité des...
Absorption effects for some elliptic equations with singularities
We give an expository review of recent results obtained for elliptic equations having natural growth terms of absorption type and singular data. As a new result, we provide an application to the case of lower order terms of subcritical growth, proving a general solvability result with measure data for a class of equations modeled on (1.6).
Abstract linear hyperbolic equations and asymptotic equivalence as
Abstract parabolic problem with non-Lipschitz nonlinearity
An abstract parabolic equation with sectorial operator and continuous nonlinearity is studied in this paper. In particular, the asymptotic behavior of solutions is described within the framework of the theory of global attractors. Examples included in the final part of the paper illustrate the presented ideas.
Abstract parabolic problems in ordered Banach spaces
We consider abstract parabolic problems in ordered Banach spaces and give conditions under which they have global attractors. Our approach is via comparison of solutions. Within this approach abstract comparison principles are obtained and bounds on the attractors are given by order intervals in Banach spaces. These results are applied to ordinary differential equations and to parabolic equations for which the main part is given by a sum of fractional powers of sectorial operators having increasing...
Abstract parabolic problems with non-Lipschitz critical nonlinearities
The Cauchy problem for a semilinear abstract parabolic equation is considered in a fractional power scale associated with a sectorial operator appearing in the linear main part of the equation. Existence of local solutions is proved for non-Lipschitz nonlinearities satisfying a certain critical growth condition.
Abstract Quasilinear Parabolic Equations.
Actuator fault tolerant control design based on a reconfigurable reference input
The prospective work reported in this paper explores a new approach to enhance the performance of an active fault tolerant control system. The proposed technique is based on a modified recovery/trajectory control system in which a reconfigurable reference input is considered when performance degradation occurs in the system due to faults in actuator dynamics. An added value of this work is to reduce the energy spent to achieve the desired closed-loop performance. This work is justified by the need...
Adaptive stabilization of continuous-time systems through a controllable modified estimation model.
Addendum to "Hölder estimates for nonlinear degenerate parabolic systems".
Addendum to "The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation"
In this addendum we address some unintentional omission in the description of the swimming model in our recent paper (Khapalov, 2013).
Addition de variables et application à la régularité
On montre dans cet article comment des théorèmes récents d’hypoellipticité ou de propagation des singularités peuvent être améliorés par une méthode d’addition de variables qui permet dans certains cas de “désingulariser” l’ensemble caractéristique.
Additional note on partial regularity of weak solutions of the Navier-Stokes equations in the class
We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution belongs to , then the set of all possible singular points of in is at most finite at every time .
Additional regularity for Lipschitz solutions of PDE.
Adiabatic approximation for a two-level atom in a light beam
Following the recent experimental realization of synthetic gauge potentials, Jean Dalibard addressed the question whether the adiabatic ansatz could be mathematically justified for a model of an atom in 2 internal states, shone by a quasi resonant laser beam. In this paper, we derive rigorously the asymptotic model guessed by the physicists, and show that this asymptotic analysis contains the information about the presence of vortices. Surprisingly, the main difficulties do not come from the nonlinear...
Admissible functions in two-scale convergence.
Admissibly integral manifolds for semilinear evolution equations
We prove the existence of integral (stable, unstable, center) manifolds of admissible classes for the solutions to the semilinear integral equation when the evolution family has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term f satisfies the (local or global) φ-Lipschitz conditions, i.e., ||f(t,x)-f(t,y)|| ≤ φ(t)||x-y|| where φ(t) belongs to some classes of admissible function spaces. These manifolds are formed by trajectories of the solutions belonging...
Alcune applicazioni della Teoria di Morse a problemi di tipo ellittico