An -existence theorem is proved for the nonlinear stationary Boltzmann equation for soft and hard forces in with given indata on the boundary, when the collision operator is truncated for small velocities.
@article{ASNSP_2002_5_1_2_359_0, author = {Arkeryd, Leif and Nouri, Anne}, title = {The stationary {Boltzmann} equation in $\mathbb {R}^n$ with given indata}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {359--385}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 1}, number = {2}, year = {2002}, mrnumber = {1991144}, zbl = {1170.76350}, language = {en}, url = {http://www.numdam.org./item/ASNSP_2002_5_1_2_359_0/} }
TY - JOUR AU - Arkeryd, Leif AU - Nouri, Anne TI - The stationary Boltzmann equation in $\mathbb {R}^n$ with given indata JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2002 SP - 359 EP - 385 VL - 1 IS - 2 PB - Scuola normale superiore UR - http://www.numdam.org./item/ASNSP_2002_5_1_2_359_0/ LA - en ID - ASNSP_2002_5_1_2_359_0 ER -
%0 Journal Article %A Arkeryd, Leif %A Nouri, Anne %T The stationary Boltzmann equation in $\mathbb {R}^n$ with given indata %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2002 %P 359-385 %V 1 %N 2 %I Scuola normale superiore %U http://www.numdam.org./item/ASNSP_2002_5_1_2_359_0/ %G en %F ASNSP_2002_5_1_2_359_0
Arkeryd, Leif; Nouri, Anne. The stationary Boltzmann equation in $\mathbb {R}^n$ with given indata. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 2, pp. 359-385. http://www.numdam.org./item/ASNSP_2002_5_1_2_359_0/
[1] On the stationary Boltzmann equation in , IMRN 12 (2000), 626-641. | MR | Zbl
,[2] On the convergence of solutions of the Enskog equation to solutions of the Boltzmann equation, Comm. Partial Differential Equations 14 (1989), 1071-1089. | MR | Zbl
- ,[3] Measure solutions of the steady Boltzmann equation in a slab, Comm. Math. Phys. 142 (1991), 285-296. | MR | Zbl
- - ,[4] The stationary Boltzmann equation in the slab with given weighted mass for hard and soft forces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 27 (1998), 533-556. | Numdam | MR | Zbl
- ,[5] solutions to the stationary Boltzmann equation in a slab, Ann. Fac. Sci. Toulouse Math. 9 (2000), 375-413. | Numdam | MR | Zbl
- ,[6] On the stationary Povzner equation in three space variables, J. Math. Kyoto Univ. 39 (1999), 115-153. | MR | Zbl
- ,[7] On the Milne problem and the hydrodynamic limit for a steady Boltzmann equation model, J. Statist. Phys. 99 (2000), 993-1019. | MR | Zbl
- ,[8] On a class of exact two-dimensional stationary solutions for the Broadwell model of the Boltzmann equation, J. Phys. A 27 (1994), 7451-7459. | MR | Zbl
- ,[9] Two-dimensional half space problems for the Broadwell discrete velocity model, Contin. Mech. Thermodyn. 8 (1996), 257-274. | MR | Zbl
- ,[10] “The mathematical theory of dilute gases”, Springer-Verlag, Berlin, 1994. | MR | Zbl
- - ,[11] Measure solutions for the steady nonlinear Boltzmann equation in a slab, Transport Theory Statist. Phys. 27 (1998), 257-271. | MR | Zbl
,[12] “A boundary value problem for the 2-dimensional Broadwell model”, Comm. Math. Phys. 114 (1985), 687-698. | MR | Zbl
- - ,[13] On non-linear stationary half-space problems in discrete kinetic theory, J. Statist. Phys. 52 (1988), 885-896. | MR | Zbl
- - - ,[14] Measure solutions for the steady linear Boltzmann equation in a slab, Transport Theory Statist. Phys. 28 (1999), 521-529. | MR | Zbl
- ,[15] Exact -dimensional solutions for two discrete velocity models with two independent densities, J. Phys. A 20 (1987), 1063-1067. | MR
,[16] On the Cauchy problem for Boltzmann equations: Global existence and weak stability, Ann. of Math. 130 (1989), 321-366. | MR | Zbl
- ,[17] regularity of velocity averages, Anal. Non Lin. 8 (1991), 271-287. | EuDML | Numdam | MR | Zbl
- - ,[18] Existence of solutions to the stationary linear Boltzmann equation, Thesis, Gothenburg, 2000. | Zbl
,[19] High frequency sound recording according to Boltzmann equation, SIAM J. Appl. Math. 14 (1966), 935-955. | MR | Zbl
,[20] Problème aux limites intérieur pour l'équation de Boltzmann en régime stationaire, faiblement non linéaire, J. Méc. Théor. Appl. 11 (1972), 183-231. | MR | Zbl
,[21] Solvability of a boundary problem for the non linear Boltzmann equation in a bounded domain, In: “Molecular Gas Dynamics” (in Russian), Aerodynamics of rarefied gases 10, 16-24, Leningrad, 1980.
,[22] Boundary value problems for the steady Boltzmann equation, J. Statist. Phys. 85 (1996), 427-454. | MR | Zbl
- ,[23] “Non linear evolution equations, Kinetic approach”, Series on Advances in Mathematics for Applied Sciences Vol. 10, World Scientific, 1993. | Zbl
,[24] The solvability of internal stationary problems for Boltzmann's equation at large Knudsen numbers, USSR Comp. Math. Math. Phys. 17 (1977), 194-204. | MR | Zbl
,[25] “On the existence of stationary solutions to the Povzner equation in a bounded domain”, 2000, submitted.
,[26] Boundary value problems for the linearized and weakly nonlinear Boltzmann equation, J. Math. Phys. 8 (1967), 1893-1898. | MR | Zbl
,[27] On convergence to equilibrium for the linear Boltzmann equation without detailed balance assumptions, Rarefied gas dynamics, Oxford UP, 19 (1995), 107-113.
,[28] A formal generalization of the H-theorem in kinetic theory, Report, Roma Tor Vergata, 1993.
,[29] Stationary solutions of the BGK model equation on a finite interval with large boundary data, Transport Theory Statist. Phys. 21 (1992), 487-500. | MR | Zbl
,[30] Steady solutions of the Boltzmann equation for a gas flow past an obstacle; I existence, Arch. Rational Mech. Anal. 84 (1983), 249-291. | MR | Zbl
- ,