Homogenization of degenerate coupled fluid flows and heat transport through porous media

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• 作者：Michal Bene&scaron ; ^a ; ^{michal.benes@cvut.cz" class="auth_mail" title="E-mail the corresponding author} ; Igor Pažanin^b
• 关键词：Nonlinear degenerate parabolic system ; Homogenization ; Asymptotic analysis ; Two-scale convergence ; Coupled transport processes in porous media
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：165-192
• 全文大小：523 K

文摘

We establish a homogenization result for a fully nonlinear degenerate parabolic system with critical growth arising from the heat and moisture flow through a partially saturated porous media. Existence of a global weak solution of the mesoscale problem is proven by means of a semidiscretization in time, a priori estimates and passing to the limit from discrete approximations. After that, porous material exhibiting periodic spatial oscillations is considered and the two-scale convergence (as the oscillation period vanishes) to a corresponding homogenized problem is rigorously proven.