We investigate limit models resulting from a dimensional analysis of quite general heterogeneous catalysis models with fast sorption (i.e. exchange of mass between the bulk phase and the catalytic surface of a reactor) and fast surface chemistry for a prototypical chemical reactor. For the resulting reaction–diffusion systems with linear boundary conditions on the normal mass fluxes, but at the same time nonlinear boundary conditions on the concentrations itself, we provide analytic properties such as local-in-time well-posedness, positivity, a priori bounds and comment on steps towards global existence of strong solutions in the class \(\mathrm {W}^{(1,2)}_p(J \times \Omega ; {{\,\mathrm{{\mathbb {R}}}\,}}^N)\), and of classical solutions in the Hölder class \(\mathrm {C}^{(1+\alpha , 2 + 2\alpha )}({\overline{J}} \times {\overline{\Omega }}; {{\,\mathrm{{\mathbb {R}}}\,}}^N)\). Exploiting that the model is based on thermodynamic principles, we further show a priori bounds related to mass conservation and the entropy principle.

我们研究了由具有普遍吸附力（即本体相与反应器的催化表面之间的质量交换）和典型化学反应器的快速表面化学作用的非常普遍的非均相催化模型的尺寸分析得出的极限模型。对于在正常质量通量上具有线性边界条件，但在浓度本身上具有非线性边界条件的反应扩散系统，我们提供了分析性质，例如局部时域适定性，正性，先验边界并对在\（\ mathrm {W} ^ {（1,2）} _ p（J \ times \ Omega; {{\，\ mathrm {{\\ mathbb {R}} } \，}} ^ N）\），以及Hölder类中的经典解\（\ mathrm {C} ^ {（1+ \ alpha，2 + 2 \ alpha}}（{\ overline {J}} \ times {\ overline {\ Omega}}; {{\，\ mathrm {{\ mathbb {R}}} \，}} ^ N）\）。利用该模型基于热力学原理，我们进一步展示了与质量守恒和熵原理有关的先验界限。