Global strong solutions for a class of heterogeneous catalysis models

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• 作者：Dieter Bothe^a ; ^{bothe@csi.tu-darmstadt.de" class="auth_mail" title="E-mail the corresponding author} ; Matthias Kö ; hne^b ; ^{koehne@math.uni-duesseldorf.de" class="auth_mail" title="E-mail the corresponding author} ; Siegfried Maier^b ; ^{maier@math.uni-duesseldorf.de" class="auth_mail" title="E-mail the corresponding author} ; Jü ; rgen Saal^b ; ^{saal@math.uni-duesseldorf.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Global existence ; Strong solution ; Chemisorption ; Diffusion&ndash ; sorption&ndash ; reaction system
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：677-709
• 全文大小：609 K

文摘

We consider a mathematical model for heterogeneous catalysis in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. The system under consideration consists of a diffusion–advection system inside the bulk phase and a reaction–diffusion–sorption system modeling the processes on the catalytic wall and the exchange between bulk and surface. We assume Fickian diffusion with constant coefficients, sorption kinetics with linear growth bound and a network of chemical reactions which possesses a certain triangular structure. Our main result gives sufficient conditions for the existence of a unique global strong L²$L^2$-solution to this model, thereby extending by now classical results on reaction–diffusion systems to the more complicated case of heterogeneous catalysis.