On the rate of convergence to equilibrium for the linear Boltzmann equation with soft potentials Cañizo Rincón, José Alfredo Einav, Amit Lods, Bertrand Functional inequalities Entropy Boltzmann equation Soft potentials In this work we present several quantitative results of convergence to equilibrium for the linear Boltzmann operator with soft potentials under Grad’s angular cut-off assumption. This is done by an adaptation of the famous entropy method and its variants, resulting in explicit algebraic, or even stretched exponential, rates of convergence to equilibrium under appropriate assumptions. The novelty in our approach is that it involves functional inequalities relating the entropy to its production rate, which have independent applications to equations with mixed linear and non-linear terms. We also briefly discuss some properties of the equation in the non-cut-off case and conjecture what we believe to be the right rate of convergence in that case. 2019-08-27T14:24:27Z 2019-08-27T14:24:27Z 2018 info:eu-repo/semantics/article Cañizo Rincón, J.A.; Einav, A.; Lods, B. On the rate of convergence to equilibrium for the linear Boltzmann equation with soft potentials. J. Math.Anal.Appl.462(2018)801–839. [https://doi.org/10.1016/j.jmaa.2017.12.052]. 0022-247X http://hdl.handle.net/10481/56651 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España Elsevier