Admissible functions in two-scale convergence.
Admissibly integral manifolds for semilinear evolution equations
We prove the existence of integral (stable, unstable, center) manifolds of admissible classes for the solutions to the semilinear integral equation when the evolution family has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term f satisfies the (local or global) φ-Lipschitz conditions, i.e., ||f(t,x)-f(t,y)|| ≤ φ(t)||x-y|| where φ(t) belongs to some classes of admissible function spaces. These manifolds are formed by trajectories of the solutions belonging...
Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation
Almost global existence of small solutions to quadratic nonlinear Schördinger equations in three space dimensions.
An adaptive numerical method for the wave equation with a nonlinear boundary condition.
An age-dependent model describing the spread of panleucopenia virus within feline populations
Global existence results and long time behavior are provided for a mathematical model describing the propagation of Feline Panleucopenia Virus (FPLV) within a domestic cat population; two transmission modes are involved: a direct one from infective cats to susceptible ones, and an indirect one from the contaminated environment to susceptible cats. A more severe impact of the virus on young cats requires an age-structured model.
An algorithm for quantum propagation through electron level crossings.
An asymptotic formula for the Green's function of an elliptic operator
An asymptotically optimal model for isotropic heterogeneous linearly elastic plates
In this paper, we derive and analyze a Reissner-Mindlin-like model for isotropic heterogeneous linearly elastic plates. The modeling procedure is based on a Hellinger-Reissner principle, which we modify to derive consistent models. Due to the material heterogeneity, the classical polynomial profiles for the plate shear stress are replaced by more sophisticated choices, that are asymptotically correct. In the homogeneous case we recover a Reissner-Mindlin model with as shear correction factor....
An asymptotically optimal model for isotropic heterogeneous linearly elastic plates
In this paper, we derive and analyze a Reissner-Mindlin-like model for isotropic heterogeneous linearly elastic plates. The modeling procedure is based on a Hellinger-Reissner principle, which we modify to derive consistent models. Due to the material heterogeneity, the classical polynomial profiles for the plate shear stress are replaced by more sophisticated choices, that are asymptotically correct. In the homogeneous case we recover a Reissner-Mindlin model with 5/6 as shear correction...
An evolutionary double-well problem
An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit
The purpose of this work is to study an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on . This allows us to connect the viscous shallow water equation and the viscous lake equations. More precisely, we study this asymptotic with well prepared data in a periodic domain looking at the influence of the variability of the depth. The result concerns weak solutions. In a second part, we discuss the general low...
An example of low Mach (Froude) number effects for compressible flows with nonconstant density (height) limit
The purpose of this work is to study an example of low Mach (Froude) number limit of compressible flows when the initial density (height) is almost equal to a function depending on x. This allows us to connect the viscous shallow water equation and the viscous lake equations. More precisely, we study this asymptotic with well prepared data in a periodic domain looking at the influence of the variability of the depth. The result concerns weak solutions. In a second part, we discuss...
Analyse limite d'équations variationnelles dans un domaine contenant une grille
Analyse précisée d'équations semi-linéaires elliptiques sur l'espace hyperbolique et application à la courbure scalaire conforme
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...
Analysis of boundary bubbling solutions for an anisotropic Emden–Fowler equation
Analysis of the self-similar solutions of a generalized Burgers equation with nonlinear damping.
Analyticity for some degenerate one-dimensional evolution equations
We study the analyticity of the semigroups generated by some degenerate second order differential operators in the space C([α,β]), where [α,β] is a bounded real interval. The asymptotic behaviour and regularity with respect to the space variable are also investigated.
Applications bilinéaires compatibles avec un opérateur hyperbolique