Mathematical aspects of the Maxwell problem

Abstract

We study the large-time behaviour of global smooth solutions to the Cauchy problem for hyperbolic regularization of conservation laws. An attracting manifold of special smooth global solutions is determined by the Chapman projection onto the phase space of consolidated variables. For small initial data we construct the Chapman projection and describe its properties in the case of the Cauchy problem for moment approximations of kinetic equations. The existence conditions for the Chapman projection are expressed in terms of the solvability of the Riccati matrix equations with parameter.

Keywords:

• closure
• the state equation
• the Chapman projection
• matrix equations
• dynamic separation

AMS Subject Classifications::

• 35-XX
• 70-XXM
• 76-XX

Acknowledgement

This work was supported by the Russian Foundation of Basic Researches (grant no. 09-01-00288).