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On halfspace problems for the weakly nonlinear discrete Boltzmann equation
1.  Department of Mathematics, Karlstad University, 651 88 Karlstad, Sweden 
[1] 
Chérif Amrouche, Yves Raudin. Singular boundary conditions and regularity for the biharmonic problem in the halfspace. Communications on Pure and Applied Analysis, 2007, 6 (4) : 957982. doi: 10.3934/cpaa.2007.6.957 
[2] 
Alexander Bobylev, Mirela Vinerean, Åsa Windfäll. Discrete velocity models of the Boltzmann equation and conservation laws. Kinetic and Related Models, 2010, 3 (1) : 3558. doi: 10.3934/krm.2010.3.35 
[3] 
Niclas Bernhoff. Boundary layers and shock profiles for the discrete Boltzmann equation for mixtures. Kinetic and Related Models, 2012, 5 (1) : 119. doi: 10.3934/krm.2012.5.1 
[4] 
Nicola Abatangelo, Serena Dipierro, Mouhamed Moustapha Fall, Sven Jarohs, Alberto Saldaña. Positive powers of the Laplacian in the halfspace under Dirichlet boundary conditions. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 12051235. doi: 10.3934/dcds.2019052 
[5] 
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 
[6] 
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. 
[7] 
Zhiming Chen, Shaofeng Fang, Guanghui Huang. A direct imaging method for the halfspace inverse scattering problem with phaseless data. Inverse Problems and Imaging, 2017, 11 (5) : 901916. doi: 10.3934/ipi.2017042 
[8] 
Yanqin Fang, Jihui Zhang. Nonexistence of positive solution for an integral equation on a HalfSpace $R_+^n$. Communications on Pure and Applied Analysis, 2013, 12 (2) : 663678. doi: 10.3934/cpaa.2013.12.663 
[9] 
Gael Diebou Yomgne. On a nonlinear Laplace equation related to the boundary Yamabe problem in the upperhalf space. Communications on Pure and Applied Analysis, 2022, 21 (2) : 517539. doi: 10.3934/cpaa.2021186 
[10] 
Weiwei Zhao, Jinge Yang, Sining Zheng. Liouville type theorem to an integral system in the halfspace. Communications on Pure and Applied Analysis, 2014, 13 (2) : 511525. doi: 10.3934/cpaa.2014.13.511 
[11] 
Chérif Amrouche, Huy Hoang Nguyen. Elliptic problems with $L^1$data in the halfspace. Discrete and Continuous Dynamical Systems  S, 2012, 5 (3) : 369397. doi: 10.3934/dcdss.2012.5.369 
[12] 
Gershon Kresin, Vladimir Maz’ya. Optimal estimates for the gradient of harmonic functions in the multidimensional halfspace. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 425440. doi: 10.3934/dcds.2010.28.425 
[13] 
Diego D. Felix, Marcelo F. Furtado, Everaldo S. Medeiros. Semilinear elliptic problems involving exponential critical growth in the halfspace. Communications on Pure and Applied Analysis, 2020, 19 (10) : 49374953. doi: 10.3934/cpaa.2020219 
[14] 
Niclas Bernhoff. Boundary layers for discrete kinetic models: Multicomponent mixtures, polyatomic molecules, bimolecular reactions, and quantum kinetic equations. Kinetic and Related Models, 2017, 10 (4) : 925955. doi: 10.3934/krm.2017037 
[15] 
Tsukasa Iwabuchi. On analyticity up to the boundary for critical quasigeostrophic equation in the half space. Communications on Pure and Applied Analysis, 2022, 21 (4) : 12091224. doi: 10.3934/cpaa.2022016 
[16] 
Marco A. Fontelos, Lucía B. Gamboa. On the structure of double layers in PoissonBoltzmann equation. Discrete and Continuous Dynamical Systems  B, 2012, 17 (6) : 19391967. doi: 10.3934/dcdsb.2012.17.1939 
[17] 
Ziwei Zhou, Jiguang Bao, Bo Wang. A Liouville theorem of parabolic MongeAmpÈre equations in halfspace. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 15611578. doi: 10.3934/dcds.2020331 
[18] 
SeungYeal Ha, Mitsuru Yamazaki. $L^p$stability estimates for the spatially inhomogeneous discrete velocity Boltzmann model. Discrete and Continuous Dynamical Systems  B, 2009, 11 (2) : 353364. doi: 10.3934/dcdsb.2009.11.353 
[19] 
TaiPing Liu, ShihHsien Yu. Boltzmann equation, boundary effects. Discrete and Continuous Dynamical Systems, 2009, 24 (1) : 145157. doi: 10.3934/dcds.2009.24.145 
[20] 
Laurent Gosse. Wellbalanced schemes using elementary solutions for linear models of the Boltzmann equation in one space dimension. Kinetic and Related Models, 2012, 5 (2) : 283323. doi: 10.3934/krm.2012.5.283 
2020 Impact Factor: 1.432
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