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On the solvability and asymptotics of the Boltzmann equation in irregular domains. (English) Zbl 0896.45007
The paper considers an initial boundary value problems for the Boltzmann equation in an irregular space domain and in an \(L^1\) setting. The authors generalize the existence results from L. Arkeryd and N. B. Maslova [J. Stat. Phys. 77, No. 5-6, 1051-1077 (1994; Zbl 0839.76073)], and the results on strong \(L^1\) asymptotics to the case of irregular domains with boundaries having finite Hausdorff measure and satisfying a cone condition. The temperature at the boundary is assumed to be constant. The boundary conditions have the regularity properties similar to Maxwellian diffuse reflection. The main results are the existence in the style of R. J. DiPerna and P. L. Lions [Ann. Math., II. Ser. 130, No. 2, 321-366 (1989; Zbl 0698.45010)], and the strong convergence to the equilibrium in \(L^1\) when the time tends to infinity.

45K05 Integro-partial differential equations
45M05 Asymptotics of solutions to integral equations
82C40 Kinetic theory of gases in time-dependent statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
Full Text: DOI
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