On some properties of linear and linearized Boltzmann collision operators for hard spheres

Pages: 521 - 555, Volume 1, Issue 4, December 2008

doi:10.3934/krm.2008.1.521       Abstract        Full Text (395.2K)       Related Articles

A. V. Bobylev - Department of Mathematics, Karlstad University, SE-65188 Karlstad, Sweden (email)
E. Mossberg - Department of Mathematics, Karlstad University, SE-65188 Karlstad, Sweden (email)

Abstract: The linear and the linearized Boltzmann collision operators for hard spheres are studied by a method based on reduction of integral equations to differential equations. We use this approach (in combination with numerical methods) to study the eigenvalues of the operators. We also use the differential equations to investigate large energy asymptotics of solutions to linear integral equations related to the Chapman-Enskog expansion.

Keywords:  Boltzmann equation, hard spheres model, eigenvalues
Mathematics Subject Classification:  82C40, 35P15, 35B40

Received: August 2008;      Revised: September 2008;      Published: October 2008.