Search results for "Equations"

On Einstein bilinear form

2012

From physical motivations and from geometrical interpretations of the Einstein equations, we give a justi cation of the non-triviality and non-degeneracy of Einstein bilinear form introduced in [1].

On the analytical expression of the multicompacton and some exact compact solutions of a nonlinear diffusive Burgers’type equation

2018

International audience; We consider the nonlinear diffusive Burgers' equation as a model equation for signals propagation on the nonlinear electrical transmission line with intersite nonlinearities. By applying the extend sine-cosine method and using an appropriate modification of the Double-Exp function method, we successfully derived on one hand the exact analytical solutions of two types of solitary waves with strictly finite extension or compact support: kinks and pulses, and on the other hand the exact solution for two interacting pulse solitary waves with compact support. These analytical results indicate that the speed of the pulse compactons doesn't depends explicitly on the pulse a…

Theoretical principles of near-field optical microscopies and spectroscopies

2000

International audience; This paper deals with the principles of detection of optical signals near a surface in a manner permitting the mapping of the distribution of the fields close to various kinds of illuminated samples. We begin with a discussion of the main physical properties of the optical fields near a surface in the absence of any probe tip. This mainly concerns phenomena involving evanescent waves for which the local decay lengths are governed not only by the sizes but also by the intrinsic properties of the surface structures. The interpretation of the detection process is reviewed on the basis of a discussion about the possibility of establishing direct comparisons between exper…

Optimal Robust Quantum Control by Inverse Geometric Optimization

2020

International audience; We develop an inverse geometric optimization technique that allows the derivation of optimal and robust exact solutions of low-dimension quantum control problems driven by external fields: we determine in the dynamical variable space optimal trajectories constrained to robust solutions by Euler-Lagrange optimization; the control fields are then derived from the obtained robust geodesics and the inverted dynamical equations. We apply this method, referred to as robust inverse optimization (RIO), to design optimal control fields producing a complete or half population transfer and a NOT quantum gate robust with respect to the pulse inhomogeneities. The method is versat…

Dynamiques de populations en milieu hétérogène : modèles et estimation de paramètres

2017

Prod 2017-344i SPE équipe EA GESTAD INRA; National audience; Cet exposé traite de (i) la modélisation de dynamiques de populations dans des paysages hétérogènes, (ii) la modélisation des paysages eux-mêmes, (iii) l'estimation des paramètres de ces modèles à partir de données d'abondance ou de données génétiques. Nous nous concentrerons sur deux grandes classes de modèles de dynamique des populations : les modèles individu-centrés basés sur des équations différentielles stochastiques, et les modèles de réaction-diffusion. Après une introduction du lien entre ces approches, 5 illustrations issues des projets sont présentées: - modélisation de paysages hétérogènes fragmentés, via l’outil MULTI…

Analysis of errors caused by incomplete knowledge of material data in mathematical models of elastic media

2011

Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation

2020

We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…

Steady‐state solutions of the aerotaxis problem

2022

We study the steady-state system of aerotaxis equations in higher dimensions.It is shown that the existence and multiplicity of solutions depend on the totalmass of the colony of bacteria, the energy function, and the boundary conditions.

Fixed point theorems for twisted (α,β)-ψ-contractive type mappings and applications

2013

The purpose of this paper is to discuss the existence and uniqueness of fixed points for new classes of mappings defined on a complete metric space. The obtained results generalize some recent theorems in the literature. Several applications and interesting consequences of our theorems are also given.

Parabolic equations with nonlinear singularities

2011

Abstract We show the existence of positive solutions u ∈ L 2 ( 0 , T ; H 0 1 ( Ω ) ) for nonlinear parabolic problems with singular lower order terms of the asymptote-type. More precisely, we shall consider both semilinear problems whose model is { u t − Δ u + u 1 − u = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , and quasilinear problems having natural growth with respect to the gradient, whose model is { u t − Δ u + ∣ ∇ u ∣ 2 u γ = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , with γ > 0 . Moreover, we prove a comparison principle and, as an application, we study the asymptotic behav…