A Polynomial Spectral Method for the Spatially Homogeneous Boltzmann Equation
نویسندگان
چکیده
منابع مشابه
Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation
For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The main technique is based on a comparison principle that uses a certain dissipative property of the linear Boltzmann equation. Implications of the technique t...
متن کاملInformation Geometry Formalism for the Spatially Homogeneous Boltzmann Equation
Information Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We review here several properties of the exponential manifold on a suitable set E of mutually absolutely continuous densities. We study in particular the fine properties of the Kullback-Liebler divergence in this context. We also ...
متن کاملAbout L P Estimates for the Spatially Homogeneous Boltzmann Equation
For the homogeneous Boltzmann equation with (cutoo or non cutoo) hard potentials, we prove estimates of propagation of L p norms with a weight (1+jxj 2) q=2 (1 < p < +1, q 2 R large enough), as well as appearance of such weights. The proof is based on some new functional inequalities for the collision operator, proven by elementary means.
متن کاملThe Spatially Homogeneous Relativistic Boltzmann Equation with a Hard Potential
In this paper, we study spatially homogeneous solutions of the Boltzmann equation in special relativity and in Robertson-Walker spacetimes. We obtain an analogue of the Povzner inequality in the relativistic case and use it to prove global existence theorems. We show that global solutions exist for a certain class of collision cross sections of the hard potential type in Minkowski space and in ...
متن کاملAnalysis of spectral methods for the homogeneous Boltzmann equation
The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2019
ISSN: 1064-8275,1095-7197
DOI: 10.1137/17m1160240