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In this paper we consider an extension of the results in shapedifferentiation of semilinear equations with smooth nonlinearity presented inJ.I. D\'iaz and D. G\'omez-Castro: An Application of Shape Differentiation tothe Effectiveness of a Steady State Reaction-Diffusion Problem Arising inChemical Engineering. Electron. J. Differ. Equations in 2015 to the case inwhich the nonlinearities might be less smooth. Namely we will show that Gateauxshape derivatives exists when the nonlinearity is only Lipschitz continuous,and we will give a definition of the derivative when the nonlinearity has ablow up. In this direction, we will study the case of root-type nonlinearities.

Shape differentiation of a steady-state reaction-diffusion problem arising in Chemical Engineering: the case of non-smooth kinetic with dead core