The heat transform and its use in thermal identification problems for electronic circuits.
The Kolmogorov equation with time-measurable coefficients.
The Method of Lines for Nonlinear Parabolic Differential Equations with Mixed Derivatives.
The method of normal splines for linear implicit differential equations of second order.
The Neumann stability of high-order symmetric schemes for convection-diffusion problems.
The version of mixed finite element methods for parabolic problems
The pressure equation in the fast diffusion range.
The quasilinear parabolic kirchhoff equation
In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.
The Riccati differential equation and a diffusion-type equation.
The speed of propagation for KPP type problems. I: Periodic framework
This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the article [7]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of the domain,...
Theorems on -dimensional Laplace transforms and their applications.
Time discretization of parabolic boundary integral equations.
Time-delay regularization of anisotropic diffusion and image processing
We study a time-delay regularization of the anisotropic diffusion model for image denoising of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell 12 (1990) 629–639], which has been proposed by Nitzberg and Shiota [IEEE Trans. Pattern Anal. Mach. Intell 14 (1998) 826–835]. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution. Finally, we show some experiments on images.
Time-delay regularization of anisotropic diffusion and image processing
We study a time-delay regularization of the anisotropic diffusion model for image denoising of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell12 (1990) 629–639], which has been proposed by Nitzberg and Shiota [IEEE Trans. Pattern Anal. Mach. Intell14 (1998) 826–835]. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution. Finally, we show some experiments on images.
Traveling waves in a one-dimensional heterogeneous medium
Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions.
Type II collapsing of maximal solutions to the Ricci flow in
Une norme « naturelle » pour la méthode des caractéristiques en éléments finis discontinus : cas 1-D
Uniform stability of linear multistep methods in Galerkin procedures for parabolic problems.
Uniqueness and stability properties of monostable pulsating fronts
We prove the uniqueness, up to shifts, of pulsating traveling fronts for reaction-diffusion equations in periodic media with Kolmogorov–Petrovskiĭ–Piskunov type nonlinearities. These results provide in particular a complete classification of all KPP pulsating fronts. Furthermore, in the more general case of monostable nonlinearities, we also derive several global stability properties and convergence to pulsating fronts for solutions of the Cauchy problem with front-like initial data. In particular,...