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Stability and bifurcation in a parabolic equation

Contributed Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 898)

Abstract

Recent results on the stability of equilibrium solutions of a parabolic equation are given with indications of the proofs. Particular attention is devoted to dependence of the stability properties on the shape of the domain and the manner in which nonhomogeneous stable equilibria can occur through a bifurcation induced by varying the domain.

Keywords

  • Stable Equilibrium
  • Equilibrium Solution
  • Unstable Manifold
  • Stable Manifold
  • Functional Differential Equation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This research was supported in part by the National Science Foundation under MCS-79-0-774, in part by the United States Army under AROD DAAG 27-79-C-0161, and in part by the United States Air Force under AF-AFOSR 76-3092C.

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© 1981 Springer-Verlag

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Hale, J.K. (1981). Stability and bifurcation in a parabolic equation. In: Rand, D., Young, LS. (eds) Dynamical Systems and Turbulence, Warwick 1980. Lecture Notes in Mathematics, vol 898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091911

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  • DOI: https://doi.org/10.1007/BFb0091911

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11171-9

  • Online ISBN: 978-3-540-38945-3

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