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In this paper, we describe the long-time behavior of the non-cutoff Boltzmann equation with soft potentials near a global Maxwellian background on the whole space in the weakly collisional limit (i.e. infinite Knudsen number $1/\nu\to…

Analysis of PDEs · Mathematics 2022-11-10 Jacob Bedrossian , Michele Coti Zelati , Michele Dolce

Efficient and accurate numerical approximation of the full Boltzmann equation has been a longstanding challenging problem in kinetic theory. This is mainly due to the high dimensionality of the problem and the complicated collision…

Numerical Analysis · Mathematics 2021-12-07 Jingwei Hu , Yubo Wang

We introduce a structured approach to the construction of linear BGK-type collision operators ensuring that the resulting Lattice-Boltzmann methods are stable with respect to a weighted $L^2$-norm. The results hold for particular boundary…

Numerical Analysis · Mathematics 2020-02-07 Philipp Otte , Martin Frank

We propose in this work a subgradient extragradient method with inertial and correction terms for solving equilibrium problems in a real Hilbert space. We obtain that the sequence generated by our proposed method converges weakly to a point…

Optimization and Control · Mathematics 2025-11-25 Chidi Elijah Nwakpa , Chinedu Izuchukwu , Chibueze CHristian Okeke , Dilber Uzun Ozsahin , Abubakar Adamu

We consider the Lame system of linear elasticity with periodically distributed inclusions whose elastic parameters have high contrast compared to the background media. We develop a unified method based on layer potential techniques to…

Analysis of PDEs · Mathematics 2022-07-13 Xin Fu , Wenjia Jing

The aim of the paper is to obtain a description of the selfadjoint subspace of the one-speed Boltzmann operator. It is proved that this subspace is nontrivial if the collision integral is polynomial and the multiplication coefficient has a…

Spectral Theory · Mathematics 2009-10-22 Roman Romanov , Michael Tihomirov

In this paper, we study the hydrodynamic and acoustic limit from Boltzmann equations for two species gas mixture with potential $\gamma \in \left(-3, 1\right]$. % in the whole space $(x \in \mathbb{R}^3)$.Here the particle masses are…

Analysis of PDEs · Mathematics 2026-03-24 Gaofeng Wang , Tianfang Wu , Linjie Xiong

The present work provides a definitive answer to the problem of quantifying relaxation to equilibrium of the solution to the spatially homogeneous Boltzmann equation for Maxwellian molecules. The beginning of the story dates back to a…

Mathematical Physics · Physics 2012-06-25 Emanuele Dolera , Eugenio Regazzini

We analytically determine all the eigenvalues and eigenfunctions of the linearized Boltzmann collision operator in massless scalar $\lambda \phi^4$ theory in the high-temperature (classical) regime. This is used to exactly compute the shear…

Nuclear Theory · Physics 2022-09-22 Gabriel S. Denicol , Jorge Noronha

We show that the widely used relaxation time approximation to the relativistic Boltzmann equation contains basic flaws, being incompatible with microscopic and macroscopic conservation laws. We propose a new approximation that fixes such…

Nuclear Theory · Physics 2021-07-28 Gabriel S. Rocha , Gabriel S. Denicol , Jorge Noronha

The recent proof of the sharp weighted bound for Calder\'on-Zygmund operators has led to much investigation in sharp mixed bounds for operators and commutators, that is, a sharp weighted bound that is a product of at least two different…

Classical Analysis and ODEs · Mathematics 2014-01-10 Theresa C. Anderson , Wendolín Damián

In this paper, we investigate the problems of Cauchy theory and exponential stability for the inhomogeneous Boltzmann equation without angular cut-off. We only deal with the physical case of hard potentials type interactions (with a…

Analysis of PDEs · Mathematics 2020-12-07 Frédéric Hérau , Daniela Tonon , Isabelle Tristani

The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…

Analysis of PDEs · Mathematics 2019-12-02 Jouko Tervo

The spectral analysis of the dissipative linear transport (Boltzmann) operator with polynomial collision integral by the Szokefalvi-Nagy - Foias functional model is given. An exact estimate for the reminder in the asymptotic of the…

Mathematical Physics · Physics 2010-07-19 Roman Romanov

Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…

Dynamical Systems · Mathematics 2025-06-06 Claire Valva , Dimitrios Giannakis

In this paper we consider a Boltzmann-type kinetic description of Follow-the-Leader traffic dynamics and we study the resulting asymptotic distributions, namely the counterpart of the Maxwellian distribution of the classical kinetic theory.…

Physics and Society · Physics 2021-07-19 Andrea Tosin , Mattia Zanella

We introduce a class of Boltzmann equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with quite general properties. By…

Probability · Mathematics 2008-10-16 Federico Bassetti , Lucia Ladelli , Daniel Matthes

The paper concerns $L^1$- convergence to equilibrium for weak solutions of the spatially homogeneous Boltzmann Equation for soft potentials $(-4\le \gm<0$), with and without angular cutoff. We prove the time-averaged $L^1$-convergence to…

Mathematical Physics · Physics 2015-05-13 Eric A. Carlen , Maria C. Carvalho , Xuguang Lu

In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth…

Analysis of PDEs · Mathematics 2015-05-20 Seok-Bae Yun

The aim of this paper is to extend to the spaces L^2(R^d , (1+|v|)^2k dv) the spectral study led in L^2(R^d , exp(|v|^2/2)dv) by R. Ellis and M. Pinsky on the space inhomogeneous linearized Boltzmann operator for hard spheres. More…

Analysis of PDEs · Mathematics 2020-10-21 Pierre Gervais