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A Boltzmanntype model for market economy and its continuous trading limit
On halfspace problems for the weakly nonlinear discrete Boltzmann equation
1.  Department of Mathematics, Karlstad University, 651 88 Karlstad, Sweden 
[1] 
Alexander Bobylev, Mirela Vinerean, Åsa Windfäll. Discrete velocity models of the Boltzmann equation and conservation laws. Kinetic & Related Models, 2010, 3 (1) : 3558. doi: 10.3934/krm.2010.3.35 
[2] 
Chérif Amrouche, Yves Raudin. Singular boundary conditions and regularity for the biharmonic problem in the halfspace. Communications on Pure & Applied Analysis, 2007, 6 (4) : 957982. doi: 10.3934/cpaa.2007.6.957 
[3] 
Niclas Bernhoff. Boundary layers and shock profiles for the discrete Boltzmann equation for mixtures. Kinetic & Related Models, 2012, 5 (1) : 119. doi: 10.3934/krm.2012.5.1 
[4] 
Davide Bellandi. On the initial value problem for a class of discrete velocity models. Mathematical Biosciences & Engineering, 2017, 14 (1) : 3143. doi: 10.3934/mbe.2017003 
[5] 
Vasily Denisov and Andrey Muravnik. On asymptotic behavior of solutions of the Dirichlet problem in halfspace for linear and quasilinear elliptic equations. Electronic Research Announcements, 2003, 9: 8893. 
[6] 
Zhiming Chen, Shaofeng Fang, Guanghui Huang. A direct imaging method for the halfspace inverse scattering problem with phaseless data. Inverse Problems & Imaging, 2017, 11 (5) : 901916. doi: 10.3934/ipi.2017042 
[7] 
Yanqin Fang, Jihui Zhang. Nonexistence of positive solution for an integral equation on a HalfSpace $R_+^n$. Communications on Pure & Applied Analysis, 2013, 12 (2) : 663678. doi: 10.3934/cpaa.2013.12.663 
[8] 
Chérif Amrouche, Huy Hoang Nguyen. Elliptic problems with $L^1$data in the halfspace. Discrete & Continuous Dynamical Systems  S, 2012, 5 (3) : 369397. doi: 10.3934/dcdss.2012.5.369 
[9] 
Gershon Kresin, Vladimir Maz’ya. Optimal estimates for the gradient of harmonic functions in the multidimensional halfspace. Discrete & Continuous Dynamical Systems  A, 2010, 28 (2) : 425440. doi: 10.3934/dcds.2010.28.425 
[10] 
Weiwei Zhao, Jinge Yang, Sining Zheng. Liouville type theorem to an integral system in the halfspace. Communications on Pure & Applied Analysis, 2014, 13 (2) : 511525. doi: 10.3934/cpaa.2014.13.511 
[11] 
Marco A. Fontelos, Lucía B. Gamboa. On the structure of double layers in PoissonBoltzmann equation. Discrete & Continuous Dynamical Systems  B, 2012, 17 (6) : 19391967. doi: 10.3934/dcdsb.2012.17.1939 
[12] 
Niclas Bernhoff. Boundary layers for discrete kinetic models: Multicomponent mixtures, polyatomic molecules, bimolecular reactions, and quantum kinetic equations. Kinetic & Related Models, 2017, 10 (4) : 925955. doi: 10.3934/krm.2017037 
[13] 
SeungYeal Ha, Mitsuru Yamazaki. $L^p$stability estimates for the spatially inhomogeneous discrete velocity Boltzmann model. Discrete & Continuous Dynamical Systems  B, 2009, 11 (2) : 353364. doi: 10.3934/dcdsb.2009.11.353 
[14] 
TaiPing Liu, ShihHsien Yu. Boltzmann equation, boundary effects. Discrete & Continuous Dynamical Systems  A, 2009, 24 (1) : 145157. doi: 10.3934/dcds.2009.24.145 
[15] 
Hui Yin, Huijiang Zhao. Nonlinear stability of boundary layer solutions for generalized BenjaminBonaMahonyBurgers equation in the half space. Kinetic & Related Models, 2009, 2 (3) : 521550. doi: 10.3934/krm.2009.2.521 
[16] 
Laurent Gosse. Wellbalanced schemes using elementary solutions for linear models of the Boltzmann equation in one space dimension. Kinetic & Related Models, 2012, 5 (2) : 283323. doi: 10.3934/krm.2012.5.283 
[17] 
Linglong Du. Characteristic half space problem for the Broadwell model. Networks & Heterogeneous Media, 2014, 9 (1) : 97110. doi: 10.3934/nhm.2014.9.97 
[18] 
Yonggang Zhao, Mingxin Wang. An integral equation involving Bessel potentials on half space. Communications on Pure & Applied Analysis, 2015, 14 (2) : 527548. doi: 10.3934/cpaa.2015.14.527 
[19] 
Michael Herty, Lorenzo Pareschi, Mohammed Seaïd. Enskoglike discrete velocity models for vehicular traffic flow. Networks & Heterogeneous Media, 2007, 2 (3) : 481496. doi: 10.3934/nhm.2007.2.481 
[20] 
Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, ChaoJiang Xu, Tong Yang. Bounded solutions of the Boltzmann equation in the whole space. Kinetic & Related Models, 2011, 4 (1) : 1740. doi: 10.3934/krm.2011.4.17 
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