# Convergence to self-similarity for ballistic annihilation dynamics

@article{Alonso2020ConvergenceTS, title={Convergence to self-similarity for ballistic annihilation dynamics}, author={Ricardo J. Alonso and V{\'e}ronique Bagland and Bertrand Lods and V{\'e}ronique Bagland}, journal={Journal de Math{\'e}matiques Pures et Appliqu{\'e}es}, year={2020} }

## 8 Citations

### A Kac Model for Kinetic Annihilation

- Mathematics, PhysicsJ. Nonlinear Sci.
- 2020

It is rigorously proved that, in some mean-field limit, a suitable hierarchy of kinetic equations is recovered for which tensorized solution to the homogenous Boltzmann with annihilation is a solution.

### Kinetic Description of a Rayleigh Gas with Annihilation

- MathematicsJournal of Statistical Physics
- 2019

In this paper, we consider the dynamics of a tagged point particle in a gas of moving hard-spheres that are non-interacting among each other. This model is known as the ideal Rayleigh gas. We add to…

### Fluid dynamic limit of Boltzmann equation for granular hard--spheres in a nearly elastic regime

- Physics, Mathematics
- 2020

In this paper, we provide the first rigorous derivation of hydrodynamic equations from the Boltzmann equation for inelastic hard spheres with small inelasticity. The hydrodynamic system that we…

### Uniform estimates on the Fisher information for solutions to Boltzmann and Landau equations

- MathematicsKinetic & Related Models
- 2019

In this note we prove that, under some minimal regularity assumptions on the initial datum, solutions to the spatially homogenous Boltzmann and Landau equations for hard potentials uniformly…

### Boundedness of meta-conformal two-point functions in one and two spatial dimensions

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

Meta-conformal invariance is a novel class of dynamical symmetries, with dynamical exponent z = 1, and distinct from the standard ortho-conformal invariance. The meta-conformal Ward identities can be…

### Inelastic Boltzmann equation driven by a particle thermal bath

- MathematicsKinetic & Related Models
- 2021

<p style='text-indent:20px;'>We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, with constant restitution coefficient <inline-formula><tex-math…

### A spectral study of the linearized Boltzmann operator in $ L^2 $-spaces with polynomial and Gaussian weights

- MathematicsKinetic & Related Models
- 2021

<p style='text-indent:20px;'>The spectrum structure of the linearized Boltzmann operator has been a subject of interest for over fifty years and has been inspected in the space…

### A Kac Model for Kinetic Annihilation

- Materials ScienceJournal of Nonlinear Science
- 2020

In this paper, we consider the stochastic dynamics of a finite system of particles in a finite volume (Kac-like particle system) which annihilate with probability α∈(0,1)\documentclass[12pt]{minimal}…

## References

SHOWING 1-10 OF 40 REFERENCES

### Probabilistic ballistic annihilation with continuous velocity distributions.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

Numerical simulations lead to the conjecture that unlike for pure annihilation (p=1), the velocity distribution becomes universal, i.e., does not depend on the initial conditions.

### Dynamics of ballistic annihilation.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

The problem of ballistically controlled annihilation is revisited for general initial velocity distributions and an arbitrary dimension and Monte Carlo and molecular dynamics simulations are implemented that turn out to be in excellent agreement with the analytical predictions.

### Kinetics and scaling in ballistic annihilation.

- PhysicsPhysical review letters
- 2002

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…

### Hydrodynamics of probabilistic ballistic annihilation.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

This work considers a dilute gas of hard spheres in dimension d> or =2 that upon collision either annihilate with probability p or undergo an elastic scattering with probability 1-p and establishes the hydrodynamic equations from the Boltzmann equation description.

### Stability, Convergence to Self-Similarity and Elastic Limit for the Boltzmann Equation for Inelastic Hard Spheres

- Mathematics
- 2009

We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients$${\alpha \in [0,1]}$$ . In the physical…

### Maxwell and very-hard-particle models for probabilistic ballistic annihilation: hydrodynamic description.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

This work focuses on simplified approaches, the Maxwell and very-hard-particle (VHP) models, which allows us to compute analytically upper and lower bounds for several quantities, and illustrates the importance of dissipation in the possible development of spatial inhomogeneities.

### Ballistic annihilation with continuous isotropic initial velocity distribution.

- PhysicsPhysical review letters
- 2001

The Boltzmann equation is solved for Maxwell particles and very hard particles in arbitrary spatial dimension and these solvable cases provide bounds for the decay exponents of the hard sphere gas.

### Dynamics of annihilation. I. Linearized Boltzmann equation and hydrodynamics.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

The linearized Boltzmann equation is solved in the hydrodynamic limit by a projection technique, which yields the evolution equations for the relevant coarse-grained fields and expressions for the transport coefficients that validate the theoretical predictions.