Wave Patterns in One-Dimensional Nonlinear Degenerate Diffusion Equations

  • Faustino Sánchez-Garduño
  • Philip K. Maini
Part of the NATO ASI Series book series (NSSA, volume 259)


Several different types of wave patterns occur in physiology, chemistry and biology. In many cases such phenomena are modelled by reactive-diffusive parabolic systems (see, for example, Fisher 1937; Kolmogorov et al. 1937; Winfree 1988; Murray 1989; Swinney & Krinsky 1992). In many biological and physical situations, dispersal is modelled by a density-dependent diffusion coefficient, for example, the bacterium Rhizobium diffuses through the roots of some leguminosae plants according to a nonlinear diffusive law (Lara-Ochoa & Bustos 1990); nonlinear diffusion has been observed in the dispersion of some insects (Okubo 1980) and small rodents (Meyers & Krebs 1974).


Phase Portrait Travel Wave Solution Wave Pattern Nonlinear Diffusion Biological Pattern Formation 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Faustino Sánchez-Garduño
    • 1
    • 2
  • Philip K. Maini
    • 1
  1. 1.Centre for Mathematical BiologyMathematical InstituteOxfordUK
  2. 2.Departamento de MatemáticasFacultad de Ciencias, UNAMC. U. MéxicoMexico

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