Diffusion on multifractals

作者：Anh V V^*; Angulo J M; Ruiz Medina M D

来源：Nonlinear Analysis-Theory Methods & Applications, 2005, 63(5-7): E2043-E2056.

DOI：10.1016/j.na.2005.02.107

• Anomalous diffusion
• Fractional diffusion
• Fractals
• Multifractals
• Generalized random fields

We introduce a class of random fields with variable mean-square regularity order defined on multifractal domains. The local singularity order of these random fields then depends on the initial variable mean-square regularity order, and on the variable local singularity exponent of the multifractal measure defining the local dimension of the domain considered. The theory is developed in a generalized framework through the covariance factorization, using the tools of reproducing kernel Hilbert spaces and fractional Sobolev spaces of variable order.

• 出版日期2005-11-30