ABSTRACT
Consider a single irreversible reaction A + B → P between mobile species that takes place inside a bounded region Ω ⊂ R 3. In practice, chemical reactions are often performed inside catalytic pellets of high porosity, hence nonlinear diffusion of the reactands has to be taken into account. If the pellet is isolated this leads to the following model problem where u 1 and u 2 denote the concentrations of A and B, respectively. ∂ u 1 ∂ t = Δ φ 1 ( u 1 ) − k r ( u 1 , u 2 ) in ( 0 , ∞ ) × Ω ∂ u 2 ∂ t = Δ φ 2 ( u 2 ) − k r ( u 1 , u 2 ) in ( 0 , ∞ ) × Ω ∂ φ 1 ( u 1 ) ∂ ν = ∂ φ 2 ( u 2 ) ∂ ν = 0 on ( 0 , ∞ ) × ∂ Ω u 1 ( 0 , ⋅ ) = u 0 , 1 , u 2 ( 0 , ⋅ ) = u 0 , 2 in Ω https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187810/28005645-324c-4d25-a9e4-00a49a74dffd/content/eqn_chapter_17_1.tif"/> with rate constant k > 0 and a continuous rate function r : ℝ + 2 → ℝ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187810/28005645-324c-4d25-a9e4-00a49a74dffd/content/inq_chapter17_215_1.tif"/> such that r(·, ·) is increasing in both variables with r(a,b) = 0 iff ab = 0; the latter is a realistic assumptions for any rate function.
