Forbidden Regions for Shock Formation in Diffusive Systems
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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