On the asymptotic limit of the effectiveness of reaction–diffusion equations in periodically structured media
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 o...
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| Published in | Journal of mathematical analysis and applications Vol. 455; no. 2; pp. 1597 - 1613 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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15.11.2017
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Gómez-Castro, D. Shaposhnikova, T.A. Díaz, J.I. Podolskii, A.V. |
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| Cites_doi | 10.1134/S1064562416020046 10.1134/S0012266111010095 10.1002/aic.690130431 10.1134/S1064562414010049 10.1007/s00024-015-1124-8 10.1134/S106456241501010X 10.1016/0022-247X(74)90025-0 10.1134/S1064562416040098 10.1134/S1064562415040110 10.4171/ZAA/146 10.1016/0009-2509(57)85028-3 10.1007/s10958-013-1253-5 10.1016/0021-9045(79)90009-1 10.1134/S106456241006027X 10.1134/S1064562415040201 10.1007/BF03377396 10.1134/S1064562417020132 10.1016/0362-546X(84)90034-8 10.1090/S0002-9939-1974-0336176-9 10.1016/0021-9045(74)90013-6 10.1016/0021-9045(68)90009-9 |
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| Keywords | p-Laplace diffusion Homogenization Effectiveness factor Non-linear boundary reaction Non-critical sizes |
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| SubjectTerms | Effectiveness factor Homogenization Non-critical sizes Non-linear boundary reaction p-Laplace diffusion |
| Title | On the asymptotic limit of the effectiveness of reaction–diffusion equations in periodically structured media |
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