We consider an integro-differential model for evolutionary gametheory which describes the evolution of a population adopting mixed strategies.Using a reformulation based on the first moments of the solution, we provesome analytical properties of the model and global estimates. The asymptoticbehavior and the stability of solutions in the case of two strategies is analyzedin details. Numerical schemes for two and three strategies which are able tocapture the correct equilibrium states are also proposed together with severalnumerical examples. © American Institute of Mathematical Sciences.

The conservation of wall paintings in archaeological sites can be difficult due to the severe damage caused by living organisms, which can degrade substrates as a result of their growth and metabolic activity. The purpose of this study was to provide information on the degradation processes affecting the artefacts of an archaeological site and to predict areas where conservation is most at risk and precarious. The study focussed on the archaeological site of Monte Sannace (Italy) and Paleopolis (Greece).

Well-balanced schemes were introduced to numerically enforce consistency with longtime behavior of the underlying continuous PDE. When applied to linear kinetic models, like the Goldstein-Taylor system, this construction generates discretizations which are inconsistent with the hydrodynamic stiff limit (despite it captures diffusive limits quite well).

In this paper, multi-disciplinary optimization techniques are applied to sail design. Two different mathematical models, providing the solution of the fluid-dynamic and the structural problems governing the behaviour of a complete sailplan, are coupled in a fluid-structure interaction (FSI) scheme, in order to determine the real flying shape of the sails and the forces acting on them. A numerical optimization algorithm is then applied, optimizing the structural pattern of the sailplan in order to maximize the driving force or other significant quantities.