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On half-space problems for the weakly non-linear 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 half-space. Communications on Pure and Applied Analysis, 2007, 6 (4) : 957-982. 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) : 35-58. 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) : 1-19. 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 half-space under Dirichlet boundary conditions. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1205-1235. 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) : 31-43. doi: 10.3934/mbe.2017003 |
[6] |
Vasily Denisov and Andrey Muravnik. On asymptotic behavior of solutions of the Dirichlet problem in half-space for linear and quasi-linear elliptic equations. Electronic Research Announcements, 2003, 9: 88-93. |
[7] |
Zhiming Chen, Shaofeng Fang, Guanghui Huang. A direct imaging method for the half-space inverse scattering problem with phaseless data. Inverse Problems and Imaging, 2017, 11 (5) : 901-916. doi: 10.3934/ipi.2017042 |
[8] |
Yanqin Fang, Jihui Zhang. Nonexistence of positive solution for an integral equation on a Half-Space $R_+^n$. Communications on Pure and Applied Analysis, 2013, 12 (2) : 663-678. doi: 10.3934/cpaa.2013.12.663 |
[9] |
Gael Diebou Yomgne. On a nonlinear Laplace equation related to the boundary Yamabe problem in the upper-half space. Communications on Pure and Applied Analysis, 2022, 21 (2) : 517-539. doi: 10.3934/cpaa.2021186 |
[10] |
Weiwei Zhao, Jinge Yang, Sining Zheng. Liouville type theorem to an integral system in the half-space. Communications on Pure and Applied Analysis, 2014, 13 (2) : 511-525. doi: 10.3934/cpaa.2014.13.511 |
[11] |
Chérif Amrouche, Huy Hoang Nguyen. Elliptic problems with $L^1$-data in the half-space. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 369-397. doi: 10.3934/dcdss.2012.5.369 |
[12] |
Gershon Kresin, Vladimir Maz’ya. Optimal estimates for the gradient of harmonic functions in the multidimensional half-space. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 425-440. 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 half-space. Communications on Pure and Applied Analysis, 2020, 19 (10) : 4937-4953. 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) : 925-955. doi: 10.3934/krm.2017037 |
[15] |
Tsukasa Iwabuchi. On analyticity up to the boundary for critical quasi-geostrophic equation in the half space. Communications on Pure and Applied Analysis, 2022, 21 (4) : 1209-1224. doi: 10.3934/cpaa.2022016 |
[16] |
Marco A. Fontelos, Lucía B. Gamboa. On the structure of double layers in Poisson-Boltzmann equation. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1939-1967. doi: 10.3934/dcdsb.2012.17.1939 |
[17] |
Ziwei Zhou, Jiguang Bao, Bo Wang. A Liouville theorem of parabolic Monge-AmpÈre equations in half-space. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 1561-1578. doi: 10.3934/dcds.2020331 |
[18] |
Seung-Yeal Ha, Mitsuru Yamazaki. $L^p$-stability estimates for the spatially inhomogeneous discrete velocity Boltzmann model. Discrete and Continuous Dynamical Systems - B, 2009, 11 (2) : 353-364. doi: 10.3934/dcdsb.2009.11.353 |
[19] |
Tai-Ping Liu, Shih-Hsien Yu. Boltzmann equation, boundary effects. Discrete and Continuous Dynamical Systems, 2009, 24 (1) : 145-157. doi: 10.3934/dcds.2009.24.145 |
[20] |
Laurent Gosse. Well-balanced schemes using elementary solutions for linear models of the Boltzmann equation in one space dimension. Kinetic and Related Models, 2012, 5 (2) : 283-323. doi: 10.3934/krm.2012.5.283 |
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