June  2008, 1(2): 295-312. doi: 10.3934/krm.2008.1.295

Qualitative analysis of the generalized Burnett equations and applications to half--space problems

1. 

Dipartimento di Matematica, Università di Parma, Italy

2. 

Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 Milano

3. 

Dipartimento di Matematica, Università di Parma, V.le G.P. Usberti 53/A, 43100 Parma

Received  March 2008 Revised  March 2008 Published  May 2008

The Generalized Burnett Equations, very recently introduced by Bobylev [3,4], are tested versus Fluid--Dynamic applications, considering the classical steady evaporation/condensation problem. By means of the methods of the qualitative theory of dynamical systems, comparison is made to other kinetic and hydrodynamic models, and indications on an appropriate choice of the disposable parameters are obtained.
Citation: Marzia Bisi, Maria Paola Cassinari, Maria Groppi. Qualitative analysis of the generalized Burnett equations and applications to half--space problems. Kinetic and Related Models, 2008, 1 (2) : 295-312. doi: 10.3934/krm.2008.1.295
[1]

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

[2]

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

[3]

Niclas Bernhoff. On half-space problems for the weakly non-linear discrete Boltzmann equation. Kinetic and Related Models, 2010, 3 (2) : 195-222. doi: 10.3934/krm.2010.3.195

[4]

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.

[5]

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

[6]

Alexander Bobylev, Åsa Windfäll. Boltzmann equation and hydrodynamics at the Burnett level. Kinetic and Related Models, 2012, 5 (2) : 237-260. doi: 10.3934/krm.2012.5.237

[7]

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

[8]

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

[9]

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

[10]

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

[11]

E. N. Dancer. Some remarks on half space problems. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 83-88. doi: 10.3934/dcds.2009.25.83

[12]

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

[13]

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

[14]

Hiroshi Inoue. Magnetic hydrodynamics equations in movingboundaries. Conference Publications, 2005, 2005 (Special) : 397-402. doi: 10.3934/proc.2005.2005.397

[15]

Linglong Du, Haitao Wang. Pointwise wave behavior of the Navier-Stokes equations in half space. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 1349-1363. doi: 10.3934/dcds.2018055

[16]

Igor Kukavica, Vlad C. Vicol. The domain of analyticity of solutions to the three-dimensional Euler equations in a half space. Discrete and Continuous Dynamical Systems, 2011, 29 (1) : 285-303. doi: 10.3934/dcds.2011.29.285

[17]

Sufang Tang, Jingbo Dou. Quantitative analysis of a system of integral equations with weight on the upper half space. Communications on Pure and Applied Analysis, 2022, 21 (1) : 121-140. doi: 10.3934/cpaa.2021171

[18]

Lei Wang, Meijun Zhu. Liouville theorems on the upper half space. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5373-5381. doi: 10.3934/dcds.2020231

[19]

Yoshihiro Ueda, Tohru Nakamura, Shuichi Kawashima. Stability of planar stationary waves for damped wave equations with nonlinear convection in multi-dimensional half space. Kinetic and Related Models, 2008, 1 (1) : 49-64. doi: 10.3934/krm.2008.1.49

[20]

Hailiang Li, Houzhi Tang, Haitao Wang. Pointwise estimates of the solution to one dimensional compressible Naiver-Stokes equations in half space. Discrete and Continuous Dynamical Systems, 2022, 42 (6) : 2603-2636. doi: 10.3934/dcds.2021205

2021 Impact Factor: 1.398

Metrics

  • PDF downloads (121)
  • HTML views (0)
  • Cited by (5)

[Back to Top]