Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.

Purpose A recursive scheme for the ALIENOR method is proposed as a remedy for the difficulties induced by the method. A progressive focusing on the most promising region, in combination with a variation of the density of the alpha-dense curve, is proposed. Design/methodology/approach ALIENOR method is aimed at reducing the space dimensions of an optimization problem by spanning it by using a single alpha-dense curve: the curvilinear abscissa along the curve becomes the only design parameter for any design space.