Related papers: Self-Similarity for Ballistic Aggregation Equation
A rotating continuum of particles attracted to each other by gravity may be modeled by the Euler-Poisson system. The existence of solutions is a very classical problem. Here it is proven that a curve of solutions exists, parametrized by the…
We study the simplest irreversible ballistically-controlled reaction, whereby particles having an initial continuous velocity distribution annihilate upon colliding. In the framework of the Boltzmann equation, expressions for the exponents…
The velocity and absorption coefficient for the plane sound waves in a classical gas are obtained by solving the Boltzmann kinetic equation, which describes the reaction of the single-particle distribution function to a periodic external…
In this study, we investigate the phenomenon of collective motion in binary mixtures of self-propelled particles. We consider two particle species, each of which consisting of pointlike objects that propel with a velocity of constant…
Theory of granular dissipative gas is discussed based on Boltzmann's equation and in view of recent experimental results in micro-gravity during few CNES and ESA campaigns [9,11]. It is recalled that the Boltzmann's distribution is a steady…
We reconsider the collapse of cosmic structures in an Einstein-de Sitter Universe, using the self similar initial conditions of Fillmore & Goldreich (1984). We first derive a new approximation to describe the dark matter dynamics in…
Aggregation of particles whose interaction potential depends on their mutual orientation is considered. The aggregation dynamics is derived using a version of Darcy's law and a variational principle depending on the geometric nature of the…
Short time existence of classical solutions is proved for a system of equations that involves a three excitations kinetic operator. The system is related to the description of a gas of bosons below but close to the critical temperature,…
We solve the one-dimensional boost-invariant kinetic equation for a relativistic massive system with the collision term treated in the relaxation time approximation. The result is an exact integral equation which can be solved numerically…
Existence of mass-conserving self-similar solutions to collision-induced breakage equation is shown for a specific class of homogeneous collision kernels and breakage functions. The proof mainly relies on a dynamical approach and…
We present a new, semi-analytic formalism to model the acceleration and collimation of relativistic jets in a gravitational potential. The gravitational energy density includes the kinetic, thermal, and electromagnetic mass contributions.…
We introduce a theory for the absorption of electromagnetic radiation by small metal particles, which generalises the random phase approximation by incorporating both electric and magnetic dipole absorption within a unified self-consistent…
In the asymptotically flat two-dimensional dilaton gravity, we present an N-body particle action which has a dilaton coupled mass term for the exact solubility. This gives nonperturbative exact solutions for the N-body self-gravitating…
We consider a one-dimensional gas of hard point particles in a finite box that are in thermal equilibrium and evolving under Hamiltonian dynamics. Tagged particle correlation functions of the middle particle are studied. For the special…
We report an experimental study of a dilute "gas" of magnetic particles subjected to a vertical alternating magnetic field in a 3D container. Due to the torque exerted by the field on the magnetic moment of each particle, a spatially…
The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under natural conditions. The distribution of any solution to the…
We survey rigorous, formal, and numerical results on the formation of point-like singularities (or blow-up) for a wide range of evolution equations. We use a similarity transformation of the original equation with respect to the blow-up…
We show the existence of self-similar solutions with constant finite mass to the time-fractional Porous-Medium Equation for all spatial dimensions $d \ge 1$ and all exponents $m>m_c=(d-2)_+/d$. This range is optimal. We find two types of…
Transport phenomena plays an important role in science and technology. In the wide variety of applications both advection and diffusion may appear. Regarding diffusion, for long times, different type of decay rates are possible for…
In this paper, we study the asymptotic behavior of solutions to a Gas-liquid model with external forces and general pressure law. Under some suitable assumptions on the initial date and $\gamma>1$, if…