Front propagation in reaction-dispersal with anomalous distributions
Grup de Física Estadística, Departament de Física, Facultat de Ciències, Edifici Cc. 08193 - Cerdanyola, Bellaterra, Spain
Corresponding author: a firstname.lastname@example.org
Revised: 7 September 2006
Published online: 8 November 2006
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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006