Registered Data

[00767] Fractal and Fractional

  • Session Time & Room : 2E (Aug.22, 17:40-19:20) @G305
  • Type : Contributed Talk
  • Abstract : Several physical and natural phenomena are characterized on one hand by the presence of different temporal and spatial scales, on the other by the presence of contacts among different components through rough interfaces like domains with non-smooth boundaries and fractal layers. The principal aim of the talk is to propose mathematical models to investigate these phenomena as well as their numerical approximation. Our attention will be focused on fractional Cauchy problems on the random Koch domains with different boundary conditions. Random Koch domains are domains whose boundary are constructed by mixtures of Koch curves with random scales. These domains are obtained as limit of domains with Lipschitz boundary whereas for the limit object, the fractal given by the random Koch domain, the boundary has Hausdorff dimension between 1 and 2. We point out that Random Koch domains provide a suitable setting to model phenomena - taking place across irregular and wild structures in which boundaries are "large" while bulk is "small"- in which the surface effects are enhanced like, for example, pulmonary system, root infiltration, tree foliage, etc..
  • Classification : 28A80, 35R11, 26A33, 35J25, 65K15
  • Format : Talk at Waseda University
  • Author(s) :
    • Raffaela Capitanelli (Sapienza University of Roma)