Governing equations and solutions of anomalous random walk limits.
Continuous time random walks model anomalous diffusion. Coupling allows the magnitude of particle jumps to depend on the waiting time between jumps. Governing equations for the long-time scaling limits of these models are found to have fractional powers of coupled space and time differential operators. Explicit solutions and scaling properties are presented for these equations, which can be used to model flow in porous media and other physical systems.
Meerschaert
Mark M
MM
Department of Mathematics, University of Nevada, Reno, NV 89557-0084, USA. mcubed@unr.edu
Benson
David A
DA
Scheffler
Hans-Peter
HP
Becker-Kern
Peter
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