Shape differentiation of steady-state reaction-diffusion problems arising in chemical engineering with non-smooth kinetics with dead core

Abstract

In this paper we consider an extension of the results in shape differentiation of semilinear equations with smooth nonlinearity presented by Diaz and Gomez-Castro [8] to the case in which the nonlinearities might be less smooth. Namely we show that Gateaux shape derivatives exists when the nonlinearity is only Lipschitz continuous, and we will give a definition of the derivative when the nonlinearity has a blow up. In this direction, we study the case of root-type nonlinearities.

Keywords

• Shape differentiation
• reaction-diffusion
• chemical engineering
• dead core