Comparison theorems for coupled reaction-diffusion equations in chemical reactor analysis (Q1310859)

The authors derive comparison theorems for systems of reaction-diffusion equations, which incorporate macro- and microstructures. The governing equations at the macrolevel are: \[ \partial_ t C_ i- D_ i \Delta C_ i+{\mathbf u}\cdot\nabla C_ i+ \int_{\partial\Omega} D_ i\partial_{\mathbf n} C_ i= F_ i(t,z,C_ j) \qquad \text{in } (0,T]\times\Lambda, \] where \(\Lambda\) is a bounded domain in \(\mathbb{R}^ n\), the \(F_ i\) are Lipschitz function in \(C_ j\) and \({\mathbf u}\) is a given velocity field. At the microlevel the equations are: \[ \partial_ t c_ i- D_ i\Delta c_ i= f_ i(t,x,c_ j) \qquad \text{in } (0,T]\times\Omega \times\Lambda. \] Here, \(\Omega\) represents the active region occupied by reactive particles in \(\Lambda\). The interaction between the two levels occurs on a part \(\Gamma\) of the boundary of \(\Omega\) via \[ D_ i\partial_{\mathbf n} C_ i= H_ i(C_ i-c_ i) \qquad \text{on } (0,T]\times \Gamma\times \Lambda, \] where the \(H_ i\) are (positive) mass transfer coefficients. Uniqueness and stability results are obtained by means of these comparison theorems.