KAUST Grant NumberKUK-I1-007-43
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AbstractWe develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf
CitationDolbeault J, Mouhot C, Schmeiser C (2015) Hypocoercivity for linear kinetic equations conserving mass. Transactions of the American Mathematical Society 367: 3807–3828. Available: http://dx.doi.org/10.1090/s0002-9947-2015-06012-7.
SponsorsThis work was partially supported by the French-Austrian Amadeus projectno. 13785UA, the ANR projects EVOL and CBDif-Fr, the Austrian Science Fund(project no. W8), and the European network DEASE. The second author thanksCambridge University for their hospitality and acknowledges support from AwardNo. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology(KAUST), as well as partial support from the ERC grant MATKIT.
PublisherAmerican Mathematical Society (AMS)