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 signicant advances in modeling these phenomena across wild media. Many problems coming from engineering, physics or biology are characterized by both the presence of dierent temporal and spatial scales and the presence of contacts among dierent components through (irregular) interfaces that often connect media with dierent 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.

The focus is on new trends on applications of fractal analysis in engineering problems This work is devoted to collect new results on Fractal applications in Engineering both from a theoretical and a numerical point of view The book is addressed to researchers in the field

Autorentext

Maria Rosaria Lancia is Professor of Mathematical Analysis at Sapienza University of Rome, where she received her PhD in Applied and Theoretical Mechanics. Her current research interests are Fractal Analysis and Numerical approximation of BVPs in fractal domains. The emphasis is on linear, quasilinear and fractional BVPs in and within fractal domains possibly with dynamical boundary conditions and vector analysis on fractafolds. She is an editorial board member of Fractal and Fractional, MDPI and of the J. of Applied Mathematics and Computation, Hill Publishing Group.
Anna Rozanova-Pierrat is Associate Professor of Applied Mathematics in CentraleSupélec, University Paris-Saclay, France. She obtained his PhD on Applied Mathematics in University Pierre et Marie Currie Paris 6 and RUDN (Moscow, Russia), where she finished her studies on Theoretical and Applied Mathematics. Her current research interests are motivated by physical and engineer problems (models of non linear acoustics, de Gennes hypothesis on the speed of the heat propagation between two media, shape optimization) involving irregular and fractal boundaries.

Inhalt

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, -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.

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