GOUDON , Thierry

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Les mathématiques, science de l'abstraction par excellence, ont pourtant des applications très concrètes : elles sont essentielles pour comprendre les problèmes planétaires actuels.

This book provides the mathematical basis for investigating numerically equations from physics, life sciences or engineering. Tools for analysis and algorithms are confronted to a large set of relevant examples that show the difficulties and the limitations of the most naïve approaches. These examples not only provide the opportunity to put...

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We investigate the behavior of solutions of simple linear kinetic equations, subjected to a strong and fast time-oscillating force field, in the diffusion regime. We consider quasiperiodic oscillations. The asymptotic behavior is governed by a convection-diffusion equation, for which we can identify the effective coefficients.

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International audience

We consider a simple model describing the interaction of a quantum particle with a vibrational environment, which eventually acts as a friction on the particle. This equation admits soliton-like solutions, and we numerically investigate their stability when subjected to a small initial impulsion. Our findings illustrate the analogies with the...

In the so-called Spitzer-Harm regime, equations of plasma physics reduce to a non linear parabolic equation for the electronic temperature. Coming back to the derivation of this limiting equation through hydrodynamic regime arguments, one is led to construct a hierarchy of models where the heat fluxes are defined through a non-local relation...

International audience

The Spitzer-Härm regime arising in plasma physics leads asymptotically to a nonlinear diffusion equation for the electron temperature. In this work we propose a hierarchy of models intended to retain more features of the underlying modeling based on kinetic equations. These models are of non--local type. Nevertheless, owing to energy...

This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the...

We go back to the analysis of the transport of (classical or quantum) particles intime-dependent random media as proposed in [F. Poupaud and A. Vasseur,J. Math. Pures Appl.(9), 82 (2003), pp. 711–748], where the convergence of the expectation of solutions of the Liouvilleequation (resp., Wigner equation) to the solution of the Fokker-Planck...

In this paper, we introduce a specific modification of the numerical fluxes in order to insure the well-balanced property of schemes on staggered grids for the Euler equations. This property is crucial for the numerical representation of equilibrium solutions of balance laws with source terms, like when describing flows subjected to gravity and...

Abstract We establish well-posedness for a model of self-propelled agents interacting through pheromone which they themselves produce. The model consists of an arbitrary number of agents modeled by a system of ordinary differential equations, for which the acceleration term includes the influence of a chemical signal, or pheromone, which...

We analyse the Landau damping mechanism for variants of Vlasov equations, with a time dependent linear force term and a self-consistent potential that involves an additional memory effect. This question is directly motivated by a model describing the interaction of particles with their environment, through momentum and energy exchanges with a...

This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the...

International audience

We investigate the stability of plane wave solutions of equations describing quantum particles interacting with a complex environment. The models take the form of PDE systems with a non local (in space or in space and time) self-consistent potential; such a coupling lead to challenging issues compared to the usual non linear Schrödinger...

The lovebirds problem consists in finding the compromise between well-being and efforts that are necessary to sustain a durable sentimental relationship. According to a modeling introduced by J.-M. Rey, the problem can be cast as to find the data for a certain dynamical system, guaranteeing that the associated trajectory belongs to the stable...

International audience

We investigate numerically the behavior of a particle, or a set of particles, which exchange momentum and energy with the environment, described as a transverse vibrational field. The large time behavior is characterized, in some specific circumstances, by means of effective friction force and Landau damping. In order to discuss these issues on...

The Spitzer-Härm regime arising in plasma physics leads asymptotically to a nonlinear diffusion equation for the electron temperature. In this work we propose a hierarchy of models intended to retain more features of the underlying modeling based on kinetic equations. These models are of non--local type. Nevertheless, owing to energy...