Forbidden Regions for Shock Formation in Diffusive Systems

Published

Journal Article

© 2015 Wiley Periodicals, Inc., A Wiley Company. We consider an initial-boundary value problem for a nonlinear parabolic system. Using perturbation methods, this problem is reduced to one of considering an evolution equation for the long-time asymptotics of the system. This model can be related to the leading order approximation for a spatially inhomogeneous reaction-diffusion system with time-dependent forcing. The evolution equation yields solutions with steady state shocks. We study some of the subtle effects introduced by time-dependent forcing. Most significant among these effects is the creation of "forbidden regions" where stationary shocks cannot form. Results are presented for bi- and tri-stable one-dimensional models as well as multidimensional systems.

Full Text

Duke Authors

Cited Authors

  • Witelski, TP; Cohen, DS

Published Date

  • October 1, 1995

Published In

Volume / Issue

  • 95 / 3

Start / End Page

  • 297 - 317

Electronic International Standard Serial Number (EISSN)

  • 1467-9590

International Standard Serial Number (ISSN)

  • 0022-2526

Digital Object Identifier (DOI)

  • 10.1002/sapm1995953297

Citation Source

  • Scopus