@article{AFST_2000_6_9_3_375_0, author = {Leif Arkeryd and Anne Nouri}, title = {$L^1$ solutions to the stationary {Boltzmann} equation in a slab}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {375--413}, publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences}, address = {Toulouse}, volume = {Ser. 6, 9}, number = {3}, year = {2000}, zbl = {0991.45005}, mrnumber = {1842024}, language = {en}, url = {https://afst.centre-mersenne.org/item/AFST_2000_6_9_3_375_0/} }
TY - JOUR AU - Leif Arkeryd AU - Anne Nouri TI - $L^1$ solutions to the stationary Boltzmann equation in a slab JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2000 SP - 375 EP - 413 VL - 9 IS - 3 PB - Université Paul Sabatier. Faculté des sciences PP - Toulouse UR - https://afst.centre-mersenne.org/item/AFST_2000_6_9_3_375_0/ LA - en ID - AFST_2000_6_9_3_375_0 ER -
%0 Journal Article %A Leif Arkeryd %A Anne Nouri %T $L^1$ solutions to the stationary Boltzmann equation in a slab %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2000 %P 375-413 %V 9 %N 3 %I Université Paul Sabatier. Faculté des sciences %C Toulouse %U https://afst.centre-mersenne.org/item/AFST_2000_6_9_3_375_0/ %G en %F AFST_2000_6_9_3_375_0
Leif Arkeryd; Anne Nouri. $L^1$ solutions to the stationary Boltzmann equation in a slab. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 9 (2000) no. 3, pp. 375-413. https://afst.centre-mersenne.org/item/AFST_2000_6_9_3_375_0/
[1] Measure solutions of the steady Boltzmann equation in a slab", Comm. Math. Phys. 142, 285-296 (1991). | MR | Zbl
), ), ). - "[2] On the solvability and asymptotics of the Boltzmann equation in irregular domains", Comm. Part. Diff. Eqs. 22, 2129-2152 (1997). | MR | Zbl
), ). - "[3] On diffuse reflection at the boundary for the Boltzmann equation and related equations", J. Stat. Phys. 77, 1051-1077 (1994). | MR | Zbl
), ). - "[4] A compactness result related to the stationary Boltzmann equation in a slab, with applications to the existence theory", Ind. Univ. Math. Journ. 44, 815-839 (1995). | MR | Zbl
), ). - "[5] Asymptotics of the Boltzmann equation with diffuse reflection boundary conditions", Mh. Math. 123, 285-298 (1997). | MR | Zbl
), ). - "[6] On the stationary Povzner equation in Rn", J. Math. Kyoto Univ. 39, 115-153 (1999). | MR | Zbl
), ). - "[7] The stationary Boltzmann equation in the slab with given weighted mass for hard and soft forces", Ann. Scuola Norm. Sup. Pisa 27, 533-556 (1998). | Numdam | MR | Zbl
), ). - "[8] On a class of exact two-dimensional stationary solutions for the Broadwell model of the Boltzmann equation", J. Phys. A, Math. Gen. 27, 7451-7459 (1994). | MR | Zbl
), ). - "[9] Two-dimensional half space problems for the Broadwell discrete velocity model", Continuum Mech. Thermodyn. 8, 257-274 (1996). | MR | Zbl
), ). - "[10] The Boltzmann equation and its applications, Springer, Berlin, 1988. | MR | Zbl
). -[11] Steady solutions of the nonlinear Boltzmann equation", Transp. Th. Stat. Phys., 27, 257-271 (1998). | MR | Zbl
). - "[12] Measure solutions of the steady linear Boltzmann equation in a slab", Transp. Th. Stat. Phys., 28, 521-529 (1999). | MR | Zbl
), -). - "[13] The mathematical theory of dilute gases, Springer, Berlin, 1994. | MR | Zbl
), ), ). -[14] A boundary value problem for the two-dimensional Broadwell model", Com. Math. Phys. 114, 687-698 (1985). | MR | Zbl
), ), ). - "[15] Exact (2+1)-dimensional solutions for two discrete velocity models with two independent densities", J. Phys. A, Math. Gen. 20, 1063-1067 (1987). | MR
). - "[16] Classification of kinetic layer problems", Comm. Pure Appl. Math. 41, 409-435 (1988). | MR | Zbl
), ), ). - "[17] On the Cauchy problem for Boltzmann equations: Global existence and weak stability", Ann. of Math. , 130, 321-366 (1989). | MR | Zbl
), ). - "[18] High frequency sound recording according to the Boltzmann equation", J. SIAM Appl. Math. 14, 935-955 (1966). | MR | Zbl
). - "[19] Problème aux limites intérieur pour l'équation de Boltzmann en régime stationnaire faiblement non linéaire", J. Mécanique, 11, 183-231 (1972). | MR | Zbl
). - "[20] Weak solutions of the Boltzmann equation", Arch. Rat. Mech. Anal. 119, 309-353 (1992). | MR | Zbl
). - "[21] Solvability of a boundary problem for the non linear Boltzmann equation in a bounded domain", Aerodynamics of rarefied gases, 10, 16-24, Leningrad Univ., Leningrad, 1980. | MR
). - "[22] Boundary value problems for the steady Boltzmann equation", J. Stat. Phys., 85, 427-454 (1996). | MR | Zbl
), ). - "[23] Dynamics of rarefied gases", Phys. Rev. 99, 1896-1897 (1955).
). - "[24] Compactness in Boltzmann's equation via Fourier integral operators and applications. I", J. Math. Kyoto Univ. 34, 391-427 (1994). | MR | Zbl
). - "[25] Existence and uniqueness of stationary solutions of the linearised Boltzmann equation in a bounded domain", Non linear evolution equations, Kinetic approach, Series on advances in Mathematics for Applied Sciences, Vol. 10, World Scientific, 1993.
). - "[26] The solvability of internal stationary problems for Boltzmann's equation at large Knudsen numbers", USSR Comp. Math. & Math. Phys. 17, 194-204 (1977). | Zbl
). - "[27] On weak-weak convergence and applications to the initial boundary value problem for kinetic equations, Preprint 35, Mathematics University of Versailles, 1999.
). -[28] Boundary value problems for the linearized and weakly nonlinear Boltzmann equation", J. Math. Phys. 8, 1893-1898 (1967). | MR | Zbl
). - "[29] On convergence to equilibrium for the linear Boltzmann equation without detailed balance assumptions", Rarefied gas dynamics 19, 107-113 (1995), Oxford UP.
). - "[30] The Boltzmann equation in kinetic theory of gases", Amer. Math. Soc. Transl. Ser. 2 47, 193-216 (1962). | MR | Zbl
). - "[31] A formal generalization of the H-theorem in kinetic theory", Report, Roma Tor Vergata, 1993.
). - "[32] Stationary solutions of the BGK model equation on a finite interval with large boundary data", Transp. Th. Stat. Phys. 21, 487-500 (1992). | MR | Zbl
). - "[33] Steady solutions of the Boltzmann equation for a gas flow past an obstacle; I Existence", Arch. Rat. Mech. Anal. 84, 249-291 (1983). | MR | Zbl
), ). - "[34] Regularity in the Boltzmann equation and the Radon transform", Comm. Part. Diff. Eqs. 19, 2057-2074 (1994). | MR | Zbl
). - "