An exactly solvable model of subdiffusion-reaction front propagation

A. A. Nepomnyashchy*, Vladimir Volpert

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

The propagation of a reaction front is considered in the framework of the Seki-Lindenberg reaction-subdiffusion model, which is appropriate in the case of a diffusion-limited reaction. Typically, this kind of problem is solved using approximate approaches or numerical methods. We apply a model piecewise linear reaction function, which allows for exact analytical solutions. For a front between two stable homogeneous states, a unique value of the front velocity is found. In the case of fronts between a stable and an unstable state, a family of traveling wave solutions is revealed. The conditions for the existence of a special 'pushed' front are considered. The influence of advection on the front velocity is also analyzed.

Original languageEnglish (US)
Article number065101
JournalJournal of Physics A: Mathematical and Theoretical
Volume46
Issue number6
DOIs
StatePublished - Feb 15 2013

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modeling and Simulation
  • Statistics and Probability

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