Math @ Duke
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Publications [#244185] of Thomas P. Witelski
search www.ams.org.Papers Published
- 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 2024/04/24)
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.
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