Front propagation in hyperbolic fractional reaction-diffusion equations

Vicenç Méndez; Vicente Ortega-Cejas

doi:https://doi.org/10.1103/PhysRevE.71.057105

Front propagation in hyperbolic fractional reaction-diffusion equations

Vicenç Méndez, Vicente Ortega-Cejas

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

Abstract

From the continuous-time random walk scheme and assuming a Lévy waiting time distribution typical of subdiffusive transport processes, we study a hyperbolic reaction-diffusion equation involving time fractional derivatives. The linear speed selection of wave fronts in this equation is analyzed. When the reaction-diffusion dimensionless number and the fractional index satisfy a certain condition, we find fronts exhibiting an unphysical behavior: they travel faster in the subdiffusive than in the diffusive regime. © 2005 The American Physical Society.

Original language	English
Article number	057105
Journal	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume	71
DOIs	https://doi.org/10.1103/PhysRevE.71.057105
Publication status	Published - 1 May 2005

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title = "Front propagation in hyperbolic fractional reaction-diffusion equations",

abstract = "From the continuous-time random walk scheme and assuming a L{\'e}vy waiting time distribution typical of subdiffusive transport processes, we study a hyperbolic reaction-diffusion equation involving time fractional derivatives. The linear speed selection of wave fronts in this equation is analyzed. When the reaction-diffusion dimensionless number and the fractional index satisfy a certain condition, we find fronts exhibiting an unphysical behavior: they travel faster in the subdiffusive than in the diffusive regime. {\textcopyright} 2005 The American Physical Society.",

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AB - From the continuous-time random walk scheme and assuming a Lévy waiting time distribution typical of subdiffusive transport processes, we study a hyperbolic reaction-diffusion equation involving time fractional derivatives. The linear speed selection of wave fronts in this equation is analyzed. When the reaction-diffusion dimensionless number and the fractional index satisfy a certain condition, we find fronts exhibiting an unphysical behavior: they travel faster in the subdiffusive than in the diffusive regime. © 2005 The American Physical Society.

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