Traveling waves in a nonlocal, piecewise linear reaction-diffusion population model


Journal Article

© 2017 IOP Publishing Ltd & London Mathematical Society. We consider an analytically tractable switching model that is a simplification of a nonlocal, nonlinear reaction-diffusion model of population growth where we take the source term to be piecewise linear. The form of this source term allows us to consider both the monostable and bistable versions of the problem. By transforming to a traveling frame and choosing specific kernel functions, we are able to reduce the problem to a system of algebraic equations. We construct solutions and examine the propagation speed and monotonicity of the resulting waves.

Full Text

Duke Authors

Cited Authors

  • Autry, EA; Bayliss, A; Volpert, VA

Published Date

  • July 21, 2017

Published In

Volume / Issue

  • 30 / 8

Start / End Page

  • 3304 - 3331

Electronic International Standard Serial Number (EISSN)

  • 1361-6544

International Standard Serial Number (ISSN)

  • 0951-7715

Digital Object Identifier (DOI)

  • 10.1088/1361-6544/aa7b95

Citation Source

  • Scopus