On the nonlinear convection-diffusion-reaction problem in a thin domain with a weak boundary absorption

Igor Pažanin; Marcone C. Pereira

doi:10.3934/cpaa.2018031

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2018, Volume 17, Issue 2: 579-592. Doi: 10.3934/cpaa.2018031

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On the nonlinear convection-diffusion-reaction problem in a thin domain with a weak boundary absorption

Igor Pažanin^1, and
Marcone C. Pereira^2,†,

1.
Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30,10000, Zagreb, Croatia
2.
Department of Applied Mathematics, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP, Brazil

^†Partially supported by CNPq 302960/2014-7 and 471210/2013-7, FAPESP 2013/22275-1, Brazil

Received: February 28, 2017

Revised: June 30, 2017

Published: June 2018

Partially supported by the Croatian Science Foundation (Grant No. 3955) and University of Zagreb (Grant No. 202778).

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Abstract

Motivated by the applications from chemical engineering, in this paper we present a rigorous derivation of the effective model describing the convection-diffusion-reaction process in a thin domain. The problem is described by a nonlinear elliptic problem with nonlinearity appearing both in the governing equation as well in the boundary condition. Using rigorous analysis in appropriate functional setting, we show that the starting singular problem posed in a two-dimensional region can be approximated with one which is regular, one-dimensional and captures the effects of all physical processes which are relevant for the original problem.

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Mathematics Subject Classification: 34B15, 35B25, 35B40, 35J91.

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Figure 1. The domain under consideration

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