Fronts in anomalous diffusion–reaction systems
Open Access
- 13 January 2013
- journal article
- review article
- Published by The Royal Society in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 371 (1982), 20120179
- https://doi.org/10.1098/rsta.2012.0179
Abstract
A review of recent developments in the field of front dynamics in anomalous diffusion–reaction systems is presented. Both fronts between stable phases and those propagating into an unstable phase are considered. A number of models of anomalous diffusion with reaction are discussed, including models with Lévy flights, truncated Lévy flights, subdiffusion-limited reactions and models with intertwined subdiffusion and reaction operators.Keywords
This publication has 63 references indexed in Scilit:
- Subdiffusion of mixed origins: When ergodicity and nonergodicity coexistPhysical Review E, 2010
- Anomalous Escape Governed by ThermalNoisePhysical Review Letters, 2007
- The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamicsJournal of Physics A: General Physics, 2004
- Front propagation into unstable statesPhysics Reports, 2003
- The random walk's guide to anomalous diffusion: a fractional dynamics approachPhysics Reports, 2000
- Wave fronts in bistable reactions with anomalous Lévy-flight diffusionPhysical Review E, 1997
- Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applicationsPhysics Reports, 1990
- Multidimensional nonlinear diffusion arising in population geneticsAdvances in Mathematics, 1978
- Fractional Brownian Motions, Fractional Noises and ApplicationsSiam Review, 1968
- THE WAVE OF ADVANCE OF ADVANTAGEOUS GENESAnnals of Eugenics, 1937