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Existence and trend to equilibrium of weak solutions of the Boltzmann equation. (English) Zbl 0907.35100

In order to eliminate some weakness concerning the initial value problem studied by R. J. DiPerna and P. L. Lions [Arch. Ration. Mech. Anal. 114, 47-55 (1991; Zbl 0724.45011)], the author makes a rigorous study of the existence and trend to equilibrium of weak solutions to the initial-boundary value problem for the nonlinear Boltzmann equation in the finite interval \(\Omega= [0,1]\). He proves crucial estimates for the solution of the problem and for the collision term of the Boltzmann equation. The asymptotic behavior of the solution as \(t\to \infty\) is also discussed with a conjecture, that the solution will tend asymptotically in time toward the non-drifting Maxwellian \(M_w(v)\).
This is an interesting paper with several remarkable results.

MSC:

35Q35 PDEs in connection with fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
35D05 Existence of generalized solutions of PDE (MSC2000)

Citations:

Zbl 0724.45011
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References:

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