2014 Madrid Conference on Applied Mathematics in honor of Alfonso Casal,
Electron. J. Diff. Eqns., Conference 22 (2015), pp. 31-45.

An application of shape differentiation to the effectiveness of a steady state reaction-diffusion problem arising in chemical engineering

Jesus Ildefonso Diaz, David Gomez-Castro

In applications it is common to arrive at a problem where the choice of an optimal domain is considered. One such problem is the one associated with the steady state reaction diffusion equation given by a semilinear elliptic equation with a monotone nonlinearity g. In some contexts, in particular in chemical engineering, it is common to consider the functional given by the integral of this nonlinear term of the solution dived by the measure of the domain $\Omega$ in which the pde takes place. This is often related with the effectiveness of the reaction. In this paper our aim is to study the differentiability of such functional as study connected to the optimality of the best chemical reactor.

Published November 20, 2015.
Math Subject Classifications: 35J61, 46G05, 35B30.
Key Words: Shape differentiation; effectiveness factor; reaction-diffusion; chemical engineering; numerical experiments.

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Jesús Ildefonso Díiaz
Departamento de Matemática Aplicada
Instituto de Matemática Interdisciplinar
Universidad Complutense de Madrid
Plaza de las Ciencias, 3, 28040 Madrid, Spain
email: jidiaz@ucm.es
David Gómez-Castro
Instituto de Matemática Interdisciplinar and Dpto. de Matemática Aplicada
Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid
Plaza de las Ciencias 3, 28040 Spain
email: dgcastro@ucm.es

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