The reactive-telegraph equation and a related kinetic model

Christopher Henderson, Panagiotis E. Souganidis

Research output: Contribution to journalArticlepeer-review


We study the long-range, long-time behavior of the reactive-telegraph equation and a related reactive-kinetic model. The two problems are equivalent in one spatial dimension. We point out that the reactive-telegraph equation, meant to model a population density, does not preserve positivity in higher dimensions. In view of this, in dimensions larger than one, we consider a reactive-kinetic model and investigate the long-range, long-time limit of the solutions. We provide a general characterization of the speed of propagation and we compute it explicitly in one and two dimensions. We show that a phase transition between parabolic and hyperbolic behavior takes place only in one dimension. Finally, we investigate the hydrodynamic limit of the limiting problem.

Original languageEnglish (US)
Article number66
JournalNonlinear Differential Equations and Applications
Issue number6
StatePublished - Dec 1 2017
Externally publishedYes


  • 35D40
  • 35F21
  • 35L15
  • 35L70
  • Primary 35F25
  • Secondary 92D25

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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