Periodic solitons and real algebraic curves.
We describe a method of calculation of all physical algebraic-geometrical solutions of KP-equations.
Periodic solutions arising in ecology of mangroves
Periodic solutions of a nonlinear evolution problem
In this paper we prove existence of periodic solutions to a nonlinear evolution system of second order partial differential equations involving the pseudo-Laplacian operator. To show the existence of periodic solutions we use Faedo-Galerkin method with a Schauder fixed point argument.
Periodic solutions of a three-species periodic reaction-diffusion system
We study a periodic reaction-diffusion system of a competitive model with Dirichlet boundary conditions. By the method of upper and lower solutions and an argument similar to that of Ahmad and Lazer, we establish the existence of periodic solutions and also investigate the stability and global attractivity of positive periodic solutions under certain conditions.
Periodic solutions of nonlinear Schrödinger equations
Periodic solutions to Maxwell equations in nonlinear media
Periodic wave solutions for the generalized shallow water wave equation by the improved Jacobi elliptic function method.
Persistance de structures géométriques dans les fluides incompressibles bidimensionnels
Persistance de structures géométriques et limite non visqueuse pour les fluides incompressibles en dimension quelconque
Persistance des structures géométriques liées aux poches de tourbillon
Persistence of solutions to nonlinear evolution equations in weighted Sobolev spaces.
Perturbation around exact solutions for nonlinear dynamical systems : application to the perturbed Burgers equation
Perturbation of a solitary wave of the nonlinear Klein-Gordon equation.
Perturbations of the harmonic map equation
We consider perturbations of the harmonic map equation in the case where the source and target manifolds are closed riemannian manifolds and the latter is in addition of nonpositive sectional curvature. For any semilinear and, under some extra conditions, quasilinear perturbation, the space of classical solutions within a homotopy class is proved to be compact. For generic perturbations the set of solutions is finite and we present a count of this set. An important ingredient for our analysis is...
Perturbations singulières des problèmes de point selle et préconditionnement du problème de Stokes
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.
Phénomène de couche limite dans un modèle de ferromagnétisme
Planar flows of incompressible heat-conducting shear-thinning fluids — existence analysis
We study the flow of an incompressible homogeneous fluid whose material coefficients depend on the temperature and the shear-rate. For large class of models we establish the existence of a suitable weak solution for two-dimensional flows of fluid in a bounded domain. The proof relies on the reconstruction of the globally integrable pressure, available due to considered Navier’s slip boundary conditions, and on the so-called -truncation method, used to obtain the strong convergence of the velocity...
Plane wave stability of some conservative schemes for the cubic Schrödinger equation
The plane wave stability properties of the conservative schemes of Besse [SIAM J. Numer. Anal.42 (2004) 934–952] and Fei et al. [Appl. Math. Comput.71 (1995) 165–177] for the cubic Schrödinger equation are analysed. Although the two methods possess many of the same conservation properties, we show that their stability behaviour is very different. An energy preserving generalisation of the Fei method with improved stability is presented.
Poche de tourbillon pour Euler 2D incompressible dans un ouvert à bord
Nous considérons l'équation d'Euler pour un fluide incompressible dans un domaine borné régulier du plan. Pour une donnée initiale avec un tourbillon de type poche, i.e valant 1 sur un ouvert lisse à bord höldérien et 0 en dehors, nous prouvons l'existence d'une solution de même type, pour tout temps si la poche initiale est décollée du bord du domaine et seulement localement en temps si la poche initiale est tangente au bord. Nous contrôlons l'influence du bord grâce à la théorie des problèmes...