A simple model for a chemical reaction is considered. The vessel where the reaction takes place is optimal if no dead core appears and if effectiveness is high. By means of the method of upper and lower solutions it is shown that, independent of the volume, sufficiently thin domains have this property. The proof is based on an estimate for the solution of the Dirichlet problem.
Cite this article
Catherine Bandle, A Note on Optimal Domains in a Reaction-Diffusion Problem. Z. Anal. Anwend. 4 (1985), no. 3, pp. 207–213DOI 10.4171/ZAA/146