An initial and boundary value problem for nonlinear composite type systems of three equations.
Analysis of a Population Model Structured by the Cells Molecular Content
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak assumptions, and deduce from it the long-time convergence. The main difficulty comes from natural degeneracy of birth terms that we overcome with a regularization technique. We then extend the results to the case with several parameters and recall the link between this...
Analytic First Integrals of Ordinary Differential Equations
Analytical solutions for the neutron transport using the spectral methods.
Analyticité locale pour les solutions de l'équation d'Euler
Anti-self-dual lagrangians : variational resolutions of non-self-adjoint equations and dissipative evolutions
Approche visqueuse de solutions discontinues de systèmes hyperboliques semilinéaires
On s’intéresse à des systèmes symétriques hyperboliques multidimensionnels en présence d’une semilinéarité. Il est bien connu que ces systèmes admettent des solutions discontinues, régulières de part et d’autre d’une hypersurface lisse caractéristique de multiplicité constante. Une telle solution étant donnée, on montre que est limite quand de solutions du système perturbé par une viscosité de taille . La preuve utilise un problème mixte parabolique et des développements de couches limites....
Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group
We propose and analyze numerical schemes for viscosity solutions of time-dependent Hamilton-Jacobi equations on the Heisenberg group. The main idea is to construct a grid compatible with the noncommutative group geometry. Under suitable assumptions on the data, the Hamiltonian and the parameters for the discrete first order scheme, we prove that the error between the viscosity solution computed at the grid nodes and the solution of the discrete problem behaves like where h is the mesh step. Such...
Approximation of solutions of nonlinear initial-value problems by B-spline functions
This note is motivated by [GGG], where an algorithm finding functions close to solutions of a given initial value-problem has been proposed (this algorithm has been recalled in Theorem 2.2). In this paper we present a commonly used definition and basic facts concerning B-spline functions and use them to improve the mentioned algorithm. This leads us to a better estimate of the Cauchy problem solution under some additional assumption on f appearing in the Cauchy problem. We also estimate the accuracy...
Asymmetric potentials and motor effect : a homogenization approach
Asymptotic solutions for large time of Hamilton–Jacobi equations in euclidean n space