Finite volume schemes for nonlinear parabolic problems: another regularization method
Finite volume schemes for the generalized subjective surface equation in image segmentation
In this paper, we describe an efficient method for 3D image segmentation. The method uses a PDE model – the so called generalized subjective surface equation which is an equation of advection-diffusion type. The main goal is to develop an efficient and stable numerical method for solving this problem. The numerical solution is based on semi-implicit time discretization and flux-based level set finite volume space discretization. The space discretization is discussed in details and we introduce three...
Finite volume schemes for the p-laplacian on cartesian meshes
This paper is concerned with the finite volume approximation of the p-laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh’s interfaces is needed in order to discretize the p-laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally...
Finite volume schemes for the p-Laplacian on Cartesian meshes
This paper is concerned with the finite volume approximation of the p-Laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh's interfaces is needed in order to discretize the p-Laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally...
Finite volumes and nonlinear diffusion equations
Finite width for a random stationary interface.
Finite-difference preconditioners for superconsistent pseudospectral approximations
The superconsistent collocation method, which is based on a collocation grid different from the one used to represent the solution, has proven to be very accurate in the resolution of various functional equations. Excellent results can be also obtained for what concerns preconditioning. Some analysis and numerous experiments, regarding the use of finite-differences preconditioners, for matrices arising from pseudospectral approximations of advection-diffusion boundary value problems, are presented...
Finite-dimensional Pullback Attractors for Non-autonomous Newton-Boussinesq Equations in Some Two-dimensional Unbounded Domains
We study the existence and long-time behavior of weak solutions to Newton-Boussinesq equations in two-dimensional domains satisfying the Poincaré inequality. We prove the existence of a unique minimal finite-dimensional pullback -attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms.
Finite-dimensional pullback attractors for parabolic equations with Hardy type potentials
Using the asymptotic a priori estimate method, we prove the existence of a pullback -attractor for a reaction-diffusion equation with an inverse-square potential in a bounded domain of (N ≥ 3), with the nonlinearity of polynomial type and a suitable exponential growth of the external force. Then under some additional conditions, we show that the pullback -attractor has a finite fractal dimension and is upper semicontinuous with respect to the parameter in the potential.
Finite-dimensionality of 2-D micropolar fluid flow with periodic boundary conditions
This paper is devoted to proving the finite-dimensionality of a two-dimensional micropolar fluid flow with periodic boundary conditions. We define the notions of determining modes and nodes and estimate their number. We check how the distribution of the forces and moments through modes influences the estimate of the number of determining modes. We also estimate the dimension of the global attractor. Finally, we compare our results with analogous results for the Navier-Stokes equation.
Finite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation
We address the problem of the existence of finite energy solitary waves for nonlinear Klein-Gordon or Schrödinger type equations in , , where . Under natural conditions on the nonlinearity , we prove the existence of in any dimension . Our result complements earlier works of Bartsch and Willem and Lorca-Ubilla where solutions invariant under the action of are constructed. In contrast, the solutions we construct are invariant under the action of where denotes the dihedral group...
Finiteness of bound states of general -body operators
Finiteness of the Lower Spectrum of Schrödinger Operators.
Finite-point extinction and continuity of interfaces in a nonlinear diffusion equation with strong absorption.
Finite-Time Blow-Up for Solutions of Nonlinear Wave Equations.
Finite-time blow-up in a two-species chemotaxis-competition model with single production
This paper is concerned with blow-up of solutions to a two-species chemotaxis-competition model with production from only one species. In previous papers there are a lot of studies on boundedness for a two-species chemotaxis-competition model with productions from both two species. On the other hand, finite-time blow-up was recently obtained under smallness conditions for competitive effects. Now, in the biological view, the production term seems to promote blow-up phenomena; this implies that the...
Finite-volume level set method and its adaptive version in completing subjective contours
In this paper we deal with a problem of segmentation (including missing boundary completion) and subjective contour creation. For the corresponding models we apply the semi-implicit finite volume numerical schemes leading to methods which are robust, efficient and stable without any restriction to a time step. The finite volume discretization enables to use the spatial adaptivity and thus improve significantly the computational time. The computational results related to image segmentation with partly...
Finite-volume solvers for a multilayer Saint-Venant system
We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to D hydrostatic Navier-Stokes equations.
Finitude d'espaces d'états liés pour certains systèmes quantiques
Finitude et classes caractéristiques pour les -modules et les faisceaux constructibles