Diffusion and Homogenization Limits with Separate Scales
作者： Naoufel Ben Abdallah , Marjolaine Puel , Michael S. Vogelius
DOI: 10.1137/110828964
关键词:
摘要: We consider the simultaneous diffusion and homogenization limit of linear Boltzmann equation in a periodic medium regime where mean free path is much smaller than lattice constant. The resulting equation, with an averaged matrix that formally obtained by first performing then one. rigorous proof relies on use two-scale limits, combination asymptotic expansion equilibrium profile powers ratio between
sci-hub.se 参考文章(17)
Carlo Cercignani, The Boltzmann equation and its applications ,(1988)
Alain Bensoussan, Alain Bensoussan, Jacques Louis Lions, George Papanicolaou, Asymptotic analysis for periodic structures ,(1978)
Otared Kavian, Introduction a LA Theorie Des Points Critiques: Et Applications Aux Problemes Elliptiques ,(1993)
Guillaume Bal, Boundary layer analysis in the homogenization of neutron transport equations in a cubic domain Asymptotic Analysis. ,vol. 20, pp. 213- 239 ,(1999)
Laurent Dumas, François Golse, Homogenization of transport equations Siam Journal on Applied Mathematics. ,vol. 60, pp. 1447- 1470 ,(2000) , 10.1137/S0036139997332087
C Bardos, F Golse, B Perthame, R Sentis, The nonaccretive radiative transfer equations: Existence of solutions and Rosseland approximation Journal of Functional Analysis. ,vol. 77, pp. 434- 460 ,(1988) , 10.1016/0022-1236(88)90096-1
Grégoire Allaire, Shape optimization by the homogenization method ,(2002)
Grégoire Allaire, Homogenization and Two-Scale Convergence SIAM Journal on Mathematical Analysis. ,vol. 23, pp. 1482- 1518 ,(1992) , 10.1137/0523084
Grégoire Allaire, Guillaume Bal, HOMOGENIZATION OF THE CRITICALITY SPECTRAL EQUATION IN NEUTRON TRANSPORT Mathematical Modelling and Numerical Analysis. ,vol. 33, pp. 721- 746 ,(1999) , 10.1051/M2AN:1999160
Remi Sentis, Approximation and Homogenization of a Transport Process Siam Journal on Applied Mathematics. ,vol. 39, pp. 134- 141 ,(1980) , 10.1137/0139011