Exponential Convergence to Equilibrium for Solutions of the Homogeneous Boltzmann Equation for Maxwellian Molecules

Emanuele Dolera
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Emanuele Dolera: Department of Mathematics, University of Pavia, Via Adolfo Ferrata 5, 27100 Pavia, Italy

Mathematics, 2022, vol. 10, issue 13, 1-11

Abstract: This paper is concerned with the spatially homogeneous Boltzmann equation, with the assumption of Maxwellian interaction. We consider initial data that belong to a small neighborhood of the equilibrium, which is a Maxwellian distribution. We prove that the solution remains in another small neighborhood with the same center and converges to this equilibrium exponentially fast, with an explicit quantification.

Keywords: Boltzmann equation; linearized Boltzmann collision operator; Maxwellian molecules; Maxwellian density function; neighborhood of equilibrium; spatially homogeneous models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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