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Inaccessible States in Time-Dependent Reaction Diffusion

Cohen, Donald S. and Witelski, Thomas P. (1996) Inaccessible States in Time-Dependent Reaction Diffusion. Studies in Applied Mathematics, 97 (4). pp. 301-319. ISSN 0022-2526. doi:10.1002/sapm1996974301.

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Using asymptotic methods we show that the long‐time dynamic behavior in certain systems of nonlinear parabolic differential equations is described by a time‐dependent, spatially inhomogeneous nonlinear evolution equation. For problems with multiple stable states, the solution develops sharp fronts separating slowly varying regions. By studying the basins of attraction of Abel's nonlinear differential equation, we demonstrate that the presence of explicit time dependence in the asymptotic evolution equation creates “forbidden regions” where the existence of interfaces is excluded. Consequently, certain configurations of stable states in the nonlinear system become inaccessible and cannot be achieved from any set of real initial conditions.

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Additional Information:© 1996 by the Massachusetts Institute of Technology. Manuscript received: 19 July 1995. D. S. C. was supported in part by the Air Force Office of Scientific Research Grant F49620-94-I-0044, National Science Foundation Grant DMS-9501511, the Department of Energy Grant W-7405-ENG-36 at the Center for Nonlinear Studies at Los Alamos, and the Director's Office (T-DO) of the Theoretical Division at Los Alamos. T. P. W. was supported by a National Science Foundation graduate fellowship. This work was performed under Air Force Office of Scientific Research Grant AFOSR-F49620-94-1-0044 and National Science Foundation Grant DMS-9501511.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)F49620-94-1-0044
Department of Energy (DOE)W-7405-ENG-36
Los Alamos National LaboratoryUNSPECIFIED
NSF Graduate Research FellowshipUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20200113-093501917
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Official Citation:Cohen, Donald S. and Witelski, Thomas P., (1996), Inaccessible States in Time‐Dependent Reaction Diffusion, Studies in Applied Mathematics, 97, doi: 10.1002/sapm1996974301
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100669
Deposited By: Tony Diaz
Deposited On:13 Jan 2020 18:16
Last Modified:16 Nov 2021 17:56

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