Comb Model with Slow and Ultraslow Diffusion

T. Sandev, A. Iomin, H. Kantz, R. Metzler, A. Chechkin, A. Nepomnyashchy, V. Volpert
2016 Mathematical Modelling of Natural Phenomena  
We consider a generalised diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyse the probability distribution functions and we derive the mean squared displacement in x and y directions. Different forms of the memory kernels (Dirac delta, power-law, and distributed order) are considered. It is shown that anomalous diffusion may occur along both x and y directions. Ultraslow diffusion and some more general diffusive processes are observed as well. We
more » ... e the corresponding continuous time random walk model for the considered two dimensional diffusion-like equation on a comb, and we derive the probability distribution functions which subordinate the process governed by this equation to the Wiener process.
doi:10.1051/mmnp/201611302 fatcat:nyo7tp52ujft5khbe4jqt5xocy