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The Maxwell problem and the Chapman projection. (English) Zbl 1283.35055

Summary: We study the large-time behavior 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.

MSC:

35L65 Hyperbolic conservation laws
35B40 Asymptotic behavior of solutions to PDEs
35Q40 PDEs in connection with quantum mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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