论文标题
随机多孔介质中线性化离子传输方程的均质化
Homogenization of the linearized ionic transport equations in random porous media
论文作者
论文摘要
In this paper we extend the homogenization results obtained in (G. Allaire, A. Mikelić, A. Piatnitski, J. Math. Phys. 51 (2010), 123103) for a system of partial differential equations describing the transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid periodic porous medium, to the case of random disperse porous media.我们介绍了一项关于随机介质中非线性泊松玻璃剂方程的研究，建立了随机均质化程序的收敛性，并证明了两尺度均质化方程的良好性。另外，在分离尺度之后，我们证明有效张量满足所谓的Onsager特性，即张量是对称和正定的。该结果表明，Onsager理论适用于随机多孔介质。还建立了磁通量的强大收敛性。
In this paper we extend the homogenization results obtained in (G. Allaire, A. Mikelić, A. Piatnitski, J. Math. Phys. 51 (2010), 123103) for a system of partial differential equations describing the transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid periodic porous medium, to the case of random disperse porous media. We present a study of the nonlinear Poisson-Boltzmann equation in a random medium, establish convergence of the stochastic homogenization procedure and prove well-posedness of the two-scale homogenized equations. In addition, after separating scales, we prove that the effective tensor satisfies the so-called Onsager properties, that is the tensor is symmetric and positive definite. This result shows that the Onsager theory applies to random porous media. The strong convergence of the fluxes is also established.
