Equivalent low-order model for a nonlinear diffusion equation

J. Farjas, J. I. Rosell, R. Herrero, R. Pons, F. Pi, G. Orriols

Research output: Contribution to journalArticleResearchpeer-review

18 Citations (Scopus)


We present an equivalent low-order model for a simple PDE system that exhibits interesting low-dimensional dynamics with a rich variety of homoclinic phenomena and whose effective dimension may be gradually increased by means of system parameters. The system is a linear heat equation subject to a nonlinear and nonlocal boundary condition and the reduction procedure is based on a finite element method. We will show that both the PDE and ODE systems have indentical stationary solution with a very similar linear stability behaviour and exhibit also very similar dynamics, at least within parameter ranges corresponding to physical devices. © 1996 Elsevier Science B.V. All rights reserved.
Original languageEnglish
Pages (from-to)107-127
JournalPhysica D: Nonlinear Phenomena
Issue number2
Publication statusPublished - 1 Jan 1996


  • Dynamical systems
  • Nonlinear partial differential equations


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