Periodic solutions of partial differential equations with hysteresis
Periodic solutions of quasilinear equations with discontinuous perturbations.
Periodic solutions of the Stefan problem with Hysteresis-Type boundary conditions.
Periodic solutions to a one-dimensional strongly nonlinear wave equation with strong dissipation
Periodic Solutions to a Parabolic Equation with Hysteresis.
Periodic systems dependent on parameters.
Periodic trajectories for evolution equations in Banach spaces.
Periodic traveling waves for a nonlocal integro-differential model.
Periodic travelling waves
Some new techniques for finding periodic travelling waves are discussed.
Periodic-Neumann boundary value problem for nonlinear parabolic equations and application to an elliptic equation
In this paper we study the periodic-Neumann boundary value problem for a class of nonlinear parabolic equations. We prove a new uniqueness result and study the structure of the set of solutions when there exist more than one solution. The ideas are applied to a Neumann problem for an elliptic equation.
Perona-Malik equation: properties of explicit finite volume scheme
The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved.
Persistence and stability for a generalized Leslie-Gower model with stage structure and dispersal.
Perturbation antisymétrique et oscillations dans des équations paraboliques
L'objet de cet exposé est l'étude d'équations d'évolution de type parabolique, périodiques, que l'on pénalise par un terme linéaire, antisymétrique. Par application des méthodes de S. Schochet pour le cas hyperbolique, on obtient un développement asymptotique des solutions de telles équations. La méthode suivie consiste à étudier l'influence de fortes oscillations en temps dans des systèmes paraboliques. Cette théorie est appliquée à deux systèmes décrivant le comportement de fluides géophysiques,...
Perturbation around exact solutions for nonlinear dynamical systems : application to the perturbed Burgers equation
Perturbations and nonlinear harmonic spaces. (Perturbations et espaces harmoniques non linéares.)
Perturbations numériques des évolutions parabolique et hyperbolique
Perturbations singulières de problèmes aux limites, non linéaires, «paraboliques dégénérés-hyperboliques»
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...