Exponential dichotomies for linear systems with impulsive effects.
Exponential expansiveness and complete admissibility for evolution families
Connections between uniform exponential expansiveness and complete admissibility of the pair are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.
Exponential stability and exponential instability for linear skew-product flows
We give characterizations for uniform exponential stability and uniform exponential instability of linear skew-product flows in terms of Banach sequence spaces and Banach function spaces, respectively. We present a unified approach for uniform exponential stability and uniform exponential instability of linear skew-product flows, extending some stability theorems due to Neerven, Datko, Zabczyk and Rolewicz.
Fonctions multisommables
La notion de multisommabilité intervient dans la théorie des équations différentielles lorsque des exponentielles d’ordres différents se mélangent. Elle a été introduite par J. Écalle et étudié récemment par plusieurs auteurs. On en donne ici une définition simple, qui fait uniquement intervenir des propriétés de décroissance exponentielle.
Generalized multitime expansions for equations with slowly varying coefficients.
Growth orders occurring in expansions of Hardy-field solutions of algebraic differential equations
Growth orders occurring in expansions of Hardy-field solutions of algebraic differential equations
We consider the asymptotic growth of Hardy-field solutions of algebraic differential equations, e.g. solutions with no oscillatory component, and prove that no ‘sub-term’ occurring in a nested expansion of such can tend to zero more rapidly than a fixed rate depending on the order of the differential equation. We also consider series expansions. An example of the results obtained may be stated as follows.Let be an element of a Hardy field which has an asymptotic series expansion in , and ,...
How frequently is a system of 2-linear Boolean equations solvable?
Influence of Vibrations on Convective Instability of Reaction Fronts in Liquids
Propagation of polymerization fronts with liquid monomer and liquid polymer is considered and the influence of vibrations on critical conditions of convective instability is studied. The model includes the heat equation, the equation for the concentration and the Navier-Stokes equations considered under the Boussinesq approximation. Linear stability analysis of the problem is fulfilled, and the convective instability boundary is found depending on...
Les formules asymptotiques pour les solutions d'un système des équations différentielles
Linear perturbations of a constant coefficient differential equation subject to mild integral smallness conditions
Local method of nonlinear analysis
Markovian Master Equations. II.
Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates
We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness ε is small with respect to the wavelength. In a previous article, we derived formally an asymptotic expansion of the solution with respect to ε using the method of matched asymptotic expansions. We also proved the existence and uniqueness of the terms of the asymptotics. In this paper, we complete the mathematical justification of our work by deriving optimal error estimates between...
Mathematical analysis of the optimizing acquisition and retention over time problem
While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer models. These models are analytically analyzed using classical, direct, methods and asymptotic expansions (for the total cost model). In...
Mathematical analysis of the optimizing acquisition and retention over time problem
While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer models. These models are analytically analyzed using classical, direct, methods and asymptotic expansions (for the total cost model). In...
Multisummability of formal power series solutions of nonlinear meromorphic differential equations
In this paper a proof is given of a theorem of J. Écalle that formal power series solutions of nonlinear meromorphic differential equations are multisummable.
Nonlinear singularly perturbed systems of differential equations: A survey.
Note on canonical forms for functional-differential equations.
Note on the asymptotic behavior of the solutions of differential equations with deviating arguments