Front propagation in reaction-dispersal with anomalous distributions
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The speed of pulled fronts for parabolic fractional-reaction-dispersal equations is derived and analyzed. From the continuous-time random walk theory we derive these equations by considering long-tailed distributions for waiting times and dispersal distances. For both cases we obtain the corresponding Hamilton-Jacobi equation and show that the selected front speed obeys the minimum action principle. We impose physical restrictions on the speeds and obtain the corresponding conditions between a dimensionless number and the fractional indexes.
PACS.05.40.Fb Random walks and Levy flights 05.60.Cd Classical transport 82.40.-g Chemical kinetics and reactions: special regimes and techniques
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