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Stability in nonlinear evolution problems by means of fixed point theorems

Jaromír J. Koliha, Ivan Straškraba (1997)

Commentationes Mathematicae Universitatis Carolinae

The stabilization of solutions to an abstract differential equation is investigated. The initial value problem is considered in the form of an integral equation. The equation is solved by means of the Banach contraction mapping theorem or the Schauder fixed point theorem in the space of functions decreasing to zero at an appropriate rate. Stable manifolds for singular perturbation problems are compared with each other. A possible application is illustrated on an initial-boundary-value problem for...

Stochastic calculus and degenerate boundary value problems

Patrick Cattiaux (1992)

Annales de l'institut Fourier

Consider the boundary value problem (L.P): ( h - A ) u = f in D , ( v - Γ ) u = g on ∂ D where A is written as A = 1 / 2 ∑ i = 1 m Y i 2 + Y 0 , and Γ is a general Venttsel’s condition (including the oblique derivative condition). We prove existence, uniqueness and smoothness of the solution of (L.P) under the Hörmander’s condition on the Lie brackets of the vector fields Y i ( 0 ≤ i ≤ m ), for regular open sets D with a non-characteristic boundary.Our study lies on the stochastic representation of u and uses the stochastic calculus of variations for the ( A , Γ ) -diffusion process...

Sur des problèmes d’asservissements stratigraphiques

Gérard Gagneux, Guy Vallet (2002)

ESAIM: Control, Optimisation and Calculus of Variations

On expose les difficultés d’ordre mathématique que posent des modèles récents de sédimentation-érosion de bassins élaborés par l’Institut Français du Pétrole et fondés sur la prise en compte de diverses contraintes d’unilatéralité. On présente quelques résultats partiels théoriques et des directions de recherche pour la résolution d’un problème inverse posé par l’étude stratigraphique d’une colonne monolithologique.

Sur des problèmes d'asservissements stratigraphiques

Gérard Gagneux, Guy Vallet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

On expose les difficultés d'ordre mathématique que posent des modèles récents de sédimentation-érosion de bassins élaborés par l'Institut Français du Pétrole et fondés sur la prise en compte de diverses contraintes d'unilatéralité. On présente quelques résultats partiels théoriques et des directions de recherche pour la résolution d'un problème inverse posé par l'étude stratigraphique d'une colonne monolithologique.

Symmetry of minimizers with a level surface parallel to the boundary

Giulio Ciraolo, Rolando Magnanini, Shigeru Sakaguchi (2015)

Journal of the European Mathematical Society

We consider the functional ℐ Ω ( v ) = ∫ Ω [ f ( | D v | ) - v ] d x , where Ω is a bounded domain and f is a convex function. Under general assumptions on f , Crasta [Cr1] has shown that if ℐ Ω admits a minimizer in W 0 1 , 1 ( Ω ) depending only on the distance from the boundary of Ω , then Ω must be a ball. With some restrictions on f , we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these...

Currently displaying 361 – 380 of 486