Abstract
<p style='text-indent:20px;'>We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, with constant restitution coefficient <inline-formula><tex-math id="M1">\begin{document}$ \alpha\in(0,1) $\end{document}</tex-math></inline-formula>, under the thermalization induced by a host medium with fixed <inline-formula><tex-math id="M2">\begin{document}$ e\in(0,1] $\end{document}</tex-math></inline-formula> and a fixed Maxwellian distribution. When the restitution coefficient <inline-formula><tex-math id="M3">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula> is close to 1 we prove existence and uniqueness of global solutions considering the close-to-equilibrium regime. We also study the long-time behaviour of these solutions and prove a convergence to equilibrium with an exponential rate.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Modeling and Simulation,Numerical Analysis
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