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On the motion of a body in thermal equilibrium immersed in a perfect gas

Kazuo Aoki, Guido Cavallaro, Carlo Marchioro, Mario Pulvirenti (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity V(t) to the limiting velocity V ∞ and prove that, under suitable smallness assumptions, the approach...

On the nonhamiltonian character of shocks in 2-D pressureless gas

Yu. G. Rykov (2002)

Bollettino dell'Unione Matematica Italiana

The paper deals with the 2-D system of gas dynamics without pressure which was introduced in 1970 by Ua. Zeldovich to describe the formation of largescale structure of the Universe. Such system occurs to be an intermediate object between the systems of ordinary differential equations and hyperbolic systems of PDE. The main its feature is the arising of singularities: discontinuities for velocity and d-functions of various types for density. The rigorous notion of generalized solutions in terms of...

On the nonlinear stabilization of the wave equation

Aissa Guesmia (1998)

Annales Polonici Mathematici

We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.

On the numerical approximation of first-order Hamilton-Jacobi equations

Rémi Abgrall, Vincent Perrier (2007)

International Journal of Applied Mathematics and Computer Science

Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.

On the persistence of decorrelation in the theory of wave turbulence

Anne-Sophie de Suzzoni (2013)

Journées Équations aux dérivées partielles

We study the statistical properties of the solutions of the Kadomstev-Petviashvili equations (KP-I and KP-II) on the torus when the initial datum is a random variable. We give ourselves a random variable u 0 with values in the Sobolev space H s with s big enough such that its Fourier coefficients are independent from each other. We assume that the laws of these Fourier coefficients are invariant under multiplication by e i θ for all θ ∈ ℝ . We investigate about the persistence of the decorrelation between the...

On the perturbation propagation in the initial-boundary value problem for quasilinear first order equations.

Yu. G. Rykov (1993)

Publicacions Matemàtiques

The paper deals with initial-boundary value problem for generalized solutions of single quasilinear nonautonomous conservation law. For the case so-called "processes with aggravation" the localization property and inner boundedness are studied. Also in case when boundary function tends to zero as t ⇒ +∞ the localization effect is regarded.

On the Picard problem for hyperbolic differential equations in Banach spaces

Antoni Sadowski (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

B. Rzepecki in [5] examined the Darboux problem for the hyperbolic equation z x y = f ( x , y , z , z x y ) on the quarter-plane x ≥ 0, y ≥ 0 via a fixed point theorem of B.N. Sadovskii [6]. The aim of this paper is to study the Picard problem for the hyperbolic equation z x y = f ( x , y , z , z x , z x y ) using a method developed by A. Ambrosetti [1], K. Goebel and W. Rzymowski [2] and B. Rzepecki [5].

On the Plasma-Charge problem

Mario Pulvirenti (2009/2010)

Séminaire Équations aux dérivées partielles

This short report is a review on recent results of S. Caprino, C. Marchioro, E. Miot and the author on the initial value problem associated to the evolution of a continuous distribution of charges (plasma) in presence of a finite number of point charges.

On the problem of symmetrization of hyperbolic equations

V. Kostin (1992)

Banach Center Publications

The aspects of symmetrization of hyperbolic equations which will be considered in this review have their own history and are related to some classical results from other areas of mathematics ([12]). Here symmetrization means representation of an initial system of equations in the form of a symmetric t-hyperbolic system in the sense of Friedrichs. Some equations of mathematical physics, for example, the equations of acoustics, of gas dynamics, etc. already have this form. In the 70's S. K. Godunov...

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