On the rate of convergence to equilibrium for the linear Boltzmann equation with soft potentials
| Autor: | Bertrand Lods, Amit Einav, José A. Cañizo |
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| Rok vydání: | 2018 |
| Předmět: |
Conjecture
Entropy (statistical thermodynamics) Functional inequalities Entropy Boltzmann equation Soft potentials Applied Mathematics 010102 general mathematics 01 natural sciences Exponential function 010101 applied mathematics symbols.namesake Rate of convergence Boltzmann constant symbols Applied mathematics 0101 mathematics Algebraic number Linear boltzmann equation Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 462:801-839 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2017.12.052 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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