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

Abstract

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.

Keywords

• Shape differentiation
• effectiveness factor
• reaction-diffusion
• chemical engineering
• numerical experiments