%0 Journal Article %1 PhysRevE.66.030102 %A Fedotov, Sergei %A Méndez, Vicenc %D 2002 %I American Physical Society %J Phys. Rev. E %K Fisher-KPP non-Markovian travelling_wave %N 3 %P 030102 %R 10.1103/PhysRevE.66.030102 %T Continuous-time random walks and traveling fronts %U http://prola.aps.org/abstract/PRE/v66/i3/e030102 %V 66 %X We present a geometric approach to the problem of propagating fronts into an unstable state, valid for an arbitrary continuous-time random walk with a Fisher–Kolmogorov-Petrovski-Piskunov growth/reaction rate. We derive an integral Hamilton-Jacobi type equation for the action functional determining the position of reaction front and its speed. Our method does not rely on the explicit derivation of a differential equation for the density of particles. In particular, we obtain an explicit formula for the propagation speed for the case of anomalous transport involving non-Markovian random processes.

@article{PhysRevE.66.030102, abstract = { We present a geometric approach to the problem of propagating fronts into an unstable state, valid for an arbitrary continuous-time random walk with a Fisher–Kolmogorov-Petrovski-Piskunov growth/reaction rate. We derive an integral Hamilton-Jacobi type equation for the action functional determining the position of reaction front and its speed. Our method does not rely on the explicit derivation of a differential equation for the density of particles. In particular, we obtain an explicit formula for the propagation speed for the case of anomalous transport involving non-Markovian random processes.}, added-at = {2010-01-18T19:09:39.000+0100}, author = {Fedotov, Sergei and M\'endez, Vicen\c{c}}, biburl = {https://www.bibsonomy.org/bibtex/2fd31739684f2b9b2c48c7ab95f4f508c/peter.ralph}, description = {Phys. Rev. E 66 (2002): Sergei Fedotov and Vicenç Méndez - Continuous-time random walks and...}, doi = {10.1103/PhysRevE.66.030102}, interhash = {f0c374417d4e6c9cc5538607a1e57974}, intrahash = {fd31739684f2b9b2c48c7ab95f4f508c}, journal = {Phys. Rev. E}, keywords = {Fisher-KPP non-Markovian travelling_wave}, month = Sep, number = 3, numpages = {4}, pages = 030102, publisher = {American Physical Society}, timestamp = {2013-09-12T22:23:01.000+0200}, title = {Continuous-time random walks and traveling fronts}, url = {http://prola.aps.org/abstract/PRE/v66/i3/e030102}, volume = 66, year = 2002 }