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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 132, Issue 1
  • February 2002, pp. 141-162

Γ-limit for the extended Fisher–Kolmogorov equation

  • D. Hilhorst (a1), L. A. Peletier (a2) and R. Schätzle (a3)
  • DOI: http://dx.doi.org/10.1017/S0308210500001566
  • Published online: 12 July 2007
Abstract

We consider the Lyapunov functional, of the rescaled Extended Fisher-Kolmogorov equation This is a fourth order generalization of the Fisher–Kolmogorov or Allen–Cahn equation. We prove that if ε → 0, then tends to the area functional in the sense of Γ-limits, where the transition energy is given by the one-dimensional kink of the Extended Fisher–Kolmogorov equation.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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