On the asymptotic limit of the effectiveness of reaction–diffusion equations in periodically structured media

• Published in: Journal of mathematical analysis and applications Vol. 455; no. 2; pp. 1597 - 1613
• Main Authors: Díaz, J.I., Gómez-Castro, D., Podolskii, A.V., Shaposhnikova, T.A.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.11.2017
• Subjects: Effectiveness factor; Homogenization; Non-critical sizes; Non-linear boundary reaction; p-Laplace diffusion; p-Laplace diffusion; Homogenization; Effectiveness factor; Non-linear boundary reaction; Non-critical sizes
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2017.06.036

This paper addresses an investigation of the asymptotic behaviour as ε→0 of the solution to the boundary value problem associated with the p-Laplace operator in an ε-periodically structured domain with a nonlinear Robin-type condition specified on the boundary of the periodic subdomains. This kind of domains include the so called perforated media as well as the case of isolated particles distributed in a periodic way. This second case arises quite often in Chemical Engineering. Here we consider a non-critical size of the particles. The objective of this paper is twofold. First we study the homogenization of solutions in the case of a continuous nonlinear reaction term on the boundary of the periodic structure. Then, we move to studying the homogenization of the effectiveness factor of the reactor, which is of relevance in Chemical Engineering.