Perturbations singulières pour une équation hyperbolique dégénérée
Perturbations singulières relatives au problème de Dirichlet dans un demi-espace
Perturbations visqueuses de problèmes mixtes hyperboliques et couches limites
Ce travail concerne le problème de Cauchy-Dirichlet pour des systèmes hyperboliques semilinéaires multidimensionnels perturbés par une “petite viscosité". Les solutions considérées sont et locales en temps, le but étant de décrire le comportement de la solution lorsque le paramètre de viscosité () tend vers zéro. Il s’agit d’un problème de perturbation singulière pour lequel une “couche limite" se forme au voisinage du bord. Par des méthodes inspirées de l’optique géométrique non linéaire, nous...
Perturbative methods in scales of Banach spaces: applications for Gevrey regularity of solutions to semilinear partial differential equations.
Perturbatively unstable eigenvalues of a periodic Schrödinger operator.
Perturbazione dello spettro dell'operatore di Laplace, in relazione ad una variazione del campo
Perturbed discrete time dynamical systems
Perturbed nonlinear degenerate problems in
Via critical point theory we establish the existence and regularity of solutions for the quasilinear elliptic problem ⎧ in ⎨ ⎩ u > 0, , where 1 < p < N; a(x) is assumed to satisfy a coercivity condition; h(x) and g(x) are not necessarily bounded but satisfy some integrability restrictions.
p-harmonic equation and quasiregular mappings
P-Harmonic obstacle problems.
Phase de diffusion pour des perturbations captives
Phase field method for mean curvature flow with boundary constraints
This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a Γ-convergence result...
Phase field method for mean curvature flow with boundary constraints
This paper is concerned with the numerical approximation of mean curvature flow t → Ω(t) satisfying an additional inclusion-exclusion constraint Ω1 ⊂ Ω(t) ⊂ Ω2. Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a Γ-convergence result...
Phase field model for mode III crack growth in two dimensional elasticity
A phase field model for anti-plane shear crack growth in two dimensional isotropic elastic material is proposed. We introduce a phase field to represent the shape of the crack with a regularization parameter and we approximate the Francfort–Marigo type energy using the idea of Ambrosio and Tortorelli. The phase field model is derived as a gradient flow of this regularized energy. We show several numerical examples of the crack growth computed with an adaptive mesh finite element method.
Phase fronts and synchronization patterns in forced oscillatory systems.
Phase Transition in multicomponent systems.
Phase transition with supercooling
L'articolo riassume il quadro dei risultati noti circa il cosiddetto problema di Stefan con sopraraffreddamento. Con ciò si intende in senso lato l'estensione del modello di Stefan a quei casi in cui la temperatura della fase liquida (solida) non è confinata al di sopra (sotto) di quella di cambiamento di fase, supposta costante. La nostra discussione è prevalentemente rivolta allo sviluppo di singolarità (non limitatezza della velocità dell'interfaccia, ecc.), al modo di prevederle, di prevenirle...
Phenomena of compensation and estimates for partial differential equations.
Phénomène de couche limite dans un modèle de ferromagnétisme
Phragmén-Lindelöf and nonexistence theorems for nonlinear elliptic equations.