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Standing pulse-like solutions of a spatially aggregating population model

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Abstract

The present paper is devoted to the study of stationary solutions of a nonlinear degenerate diffusion equation involving a nonlocal convection term, which represents a mathematical model for spatially aggregating phenomena of populations. The equation has two ecological parameters:m>1 for the diffusion process and 0≦r≦∞ for the aggregating process expressed by the convection term. For the special case ofm=2, this paper gives all stationary solutions of the one-parameter family {P(2,r)} of the equations. The result asserts thatP(2,r) has no non-trivial stationary solution when\(0 \leqq r \leqq \sqrt 2 \), whileP(2,r) has many pulse-like stationary solutions when\(r > \sqrt 2 \). The paper also states a partial result for the general case ofm, and offers a view of the global structure of stationary solutions ofP(m, r).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ehime University, 790, Matsuyama, Japan

    Tsutomu Ikeda

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  1. Tsutomu Ikeda
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Ikeda, T. Standing pulse-like solutions of a spatially aggregating population model. Japan J. Appl. Math. 2, 111–149 (1985). https://doi.org/10.1007/BF03167041

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  • DOI: https://doi.org/10.1007/BF03167041

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