ON THE INELASTIC BOLTZMANN EQUATION FOR SOFT POTENTIALS WITH DIFFUSION

被引：1

作者：

Meng, Fei ^{[1
]}

Liu, Fang ^{[2
]}

机构：

[1] Nanjing Univ Posts & Telecommun, Sch Sci, Nanjing 210023, Peoples R China

[2] Nanjing Univ Sci & Technol, Sch Sci, Dept Math, Nanjing 210094, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2020年 / 19卷 / 11期

关键词：

Boltzmann equations; inelastic collisions; granular flows; heat bath; soft potentials; non-constant restitution coefficent; SPATIALLY HOMOGENEOUS BOLTZMANN; COOLING PROCESS; GRANULAR GASES; HARD-SPHERES; EXISTENCE; METRICS; MODEL;

D O I：

10.3934/cpaa.2020233

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with the Cauchy problem of the inelastic Boltzmann equation for soft potentials, with a Laplace term representing the random background forcing. The inelastic interaction here is characterized by the nonconstant restitution coefficient. We prove that under the assumption that the initial datum has bounded mass, energy and entropy, there exists a weak solution to this equation. The smoothing effect of weak solutions is also studied. In addition, it is shown the solution is unique and stable with respect to the initial datum provided that the initial datum belongs to L-2 (R-3).

引用

页码：5197 / 5217

页数：21

共 26 条

[1] Boltzmann Model for Viscoelastic Particles: Asymptotic Behavior, Pointwise Lower Bounds and Regularity [J].

Alonso, R. ;

Lods, B. .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2014, 331 (02) :545-591

[2] Two proofs of Haft's law for dissipative gases: The use of entropy and the weakly inelastic regime [J].

Alonso, Ricardo J. ;

Lods, Bertrand .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 397 (01) :260-275

[3] FREE COOLING AND HIGH-ENERGY TAILS OF GRANULAR GASES WITH VARIABLE RESTITUTION COEFFICIENT [J].

Alonso, Ricardo J. ;

Lods, Bertrand .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2010, 42 (06) :2499-2538

[4] Convolution Inequalities for the Boltzmann Collision Operator [J].

Alonso, Ricardo J. ;

Carneiro, Emanuel ;

Gamba, Irene M. .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2010, 298 (02) :293-322

[5] Existence of Global Solutions to the Cauchy Problem for the Inelastic Boltzmann Equation with Near-vacuum Data [J].

Alonso, Ricardo J. .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2009, 58 (03) :999-1022

[6] Decay rates in probability metrics towards homogeneous cooling states for the inelastic Maxwell model [J].

Bisi, M. ;

Carrillo, J. A. ;

Toscani, G. .

JOURNAL OF STATISTICAL PHYSICS, 2006, 124 (2-4) :625-653

[7] Contractive metrics for a Boltzmann equation for granular gases: Diffusive equilibria [J].

Bisi, M ;

Carrillo, JA ;

Toscani, G .

JOURNAL OF STATISTICAL PHYSICS, 2005, 118 (1-2) :301-331

[8] On some properties of kinetic and hydrodynamic equations for inelastic interactions [J].

Bobylev, AV ;

Carrillo, JA ;

Gamba, IM .

JOURNAL OF STATISTICAL PHYSICS, 2000, 98 (3-4) :743-773

[9] Self-similar asymptotics for the Boltzmann equation with inelastic and elastic interactions [J].

Bobylev, AV ;

Cercignani, C .

JOURNAL OF STATISTICAL PHYSICS, 2003, 110 (1-2) :333-375

[10] Moment equations for a granular material in a thermal bath [J].

Bobylev, AV ;

Cercignani, C .

JOURNAL OF STATISTICAL PHYSICS, 2002, 106 (3-4) :547-567

← 1 2 3 →