Abstract
For solutions of reaction-diffusion systems under Dirichlet or Neumann boundary conditions, having a small parameter ε as a coefficient to the time derivative of the first component, the principal term of the asymptotics with respect to ε is found for all t>0. This principal term is a solution of the system, obtained as a limit for ε=0, and has a finite number of discontinuities; the continuous parts, beginning from the second, are situated on finite-dimensional unstable manifolds passing through stationary points of the limit system. Bibliography: 4 titles.
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Literature Cited
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Additional information
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 17, pp. 128–152, 1994.
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Vishik, M.I., Skvortzov, V.Y. Stabilized Asymptotics of solutions to reaction-diffusion systems with a small parameter. J Math Sci 75, 1698–1714 (1995). https://doi.org/10.1007/BF02368671
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DOI: https://doi.org/10.1007/BF02368671