Duke Applied Mathematics

Publications [#244185] of Thomas P. Witelski

Papers Published

1. Witelski, TP; Cohen, DS, Forbidden Regions for Shock Formation in Diffusive Systems, Studies in Applied Mathematics, vol. 95 no. 3 (October, 1995), pp. 297-317, WILEY, ISSN 0022-2526 [Gateway.cgi], [doi]
   (last updated on 2026/01/19)

   Abstract:
   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.