Fractals in Engineering: Theoretical Aspects and Numerical Approximations

Fractal structures or geometries currently play a key role in all models for natural and industrial processes that exhibit the formation of rough surfaces and interfaces. Computer simulations, analytical theories and experiments have led to signi?cant advances in modeling these phenomena across wild media. Many problems coming from engineering, physics or biology are characterized by both the presence of di?erent temporal and spatial scales and the presence of contacts among di?erent components through (irregular) interfaces that often connect media with di?erent characteristics. This work is devoted to collecting new results on fractal applications in engineering from both theoretical and numerical perspectives. The book is addressed to researchers in the field.

C. Alberini and S. Finzi Vita, A numerical approach to a nonlinear diffusion model for self-organised criticality phenomena.- M. Cefalo et al., Approximation of 3D Stokes flows in fractal domains.- S. Fragapane, 8-Laplacian obstacle problems in fractal domains.- M. Gabbard, Discretization of the Koch Snowflake Domain with Boundary and Interior Energies.- M.V. Marchi, On the dimension of the Sierpinski gasket in l2.- U. Mosco and M.A. Vivaldi, On the external approximation of Sobolev spaces by M-convergence.- A. Rozanova-Pierrat, Generalization of Rellich-Kondrachov theorem and trace compacteness for  fractal boundaries.