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An example of nonlinear toxic mass spreading

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Abstract

A one-dimensional, nonlinear problem of reproductive toxic mass spreading is studied in this paper. The nonlinearity is due to the difference of the reproduction rates in the toxic region and the nontoxic region. Multiple steady state solutions are found and their stability and instability are proved. Due to the instability, there may exist turning points (also called saddle-node bifurcation points), at which an infinitesimal perturbation of some parameters may cause a catastrophic change in the location of the steady state toxic front (the interface of the toxic region and the nontoxic region). For the time dependent case, the propagation of the toxic front is considered. An integral equation is derived to determine the propagation of the toxic front. Some numerical results are found for a specific example.

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Author notes

  1. S. S. P. Shen

    Present address: Department of Mathematics, University of Saskatchewan, S7N 0W0, Saskatoon, Saskatchewan, Canada

Authors and Affiliations

  1. Department of Mathematics and Climate System Research Program, College of Geosciences, USA

    S. S. P. Shen

  2. Department of Mathematics, Texas A&M University, 77843, College Station, TX, USA

    W. L. Perry

Authors
  1. S. S. P. Shen
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  2. W. L. Perry
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Shen, S.S.P., Perry, W.L. An example of nonlinear toxic mass spreading. Applied Scientific Research 47, 323–339 (1990). https://doi.org/10.1007/BF00386242

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  • DOI: https://doi.org/10.1007/BF00386242

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