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A new traveling-wave solution of Fisher's equation with density-dependent diffusivity

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Abstract

A new traveling-wave solution of Fisher's equation is found when the diffusivity is taken to be a smoothed step function of the dependent variable. The form of the solution and a necessary relationship between the traveling wave's speed and the diffusivity are predicted. This is done using flux continuity considerations in the limit when the diffusivity is piecewise constant. The predicted form is verified by numerical integration of the equation with a slightly smoothed step function diffusivity.

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Author notes

  1. C. K. Hayes

    Present address: Xon Tech Inc., 6862 Hayvenhurst Avenue, 91406, Van Nuys, CA, USA

Authors and Affiliations

  1. Department of Applied Mathematics, California Institute of Technology, CA, Pasadena, 91125, USA

    C. K. Hayes

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  1. C. K. Hayes
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Additional information

Work performed under the auspices of the US Army Research Office (Durham), Contract DAAL03-89-K-0014; the National Science Foundation, Grant DMS87-06642; and the Air Force Office of Scientific Research, Grant AFOSR-88-0269

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Hayes, C.K. A new traveling-wave solution of Fisher's equation with density-dependent diffusivity. J. Math. Biol. 29, 531–537 (1991). https://doi.org/10.1007/BF00164050

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  • DOI: https://doi.org/10.1007/BF00164050

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