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Asymptotic Behavior of the interfaces to a nonlinear degenerate diffusion equation in population dynamics

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Abstract

We consider a spatially aggregating population model which is governed by a nonlinear degenerate diffusion and advection equation. The interface in this model implies the time-dependent boundary between the populated region and the unpopulated one. The asymptotic behavior of the interface is almost completely investigated.

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References

  1. W. Alt, Contraction patterns in a viscous polymer system. to appear in Lecture Notes in Biomath.,55, 1984.

  2. D. G. Aronson, Regularity properties of flows through porous media: The interface. Arch. Rational Mech. Anal.,37 (1970), 1–10.

    Article  MATH  MathSciNet  Google Scholar 

  3. L. A. Caffarelli and A. Friedman, Regularity of the free boundary for the one-dimensional flow of gas in a porous media. Amer. J. Math.,101 (1979), 1193–1218.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Friedman, Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs, N. J., 1964.

    MATH  Google Scholar 

  5. A. Friedman, Partial Differential Equations. Holt, Rinehart and Winston, New York, 1969.

    MATH  Google Scholar 

  6. W. D. Hamilton, Geometry for the selfish herd. J. Theoret. Biol.,31 (1971), 295–311.

    Article  Google Scholar 

  7. B. F. Knerr, The porous media equation in one dimension. Trans. Amer. Math. Soc.,234 (1977), 381–415.

    Article  MATH  MathSciNet  Google Scholar 

  8. O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural’ceva, Linear and Quasilinear Equations of Parabolic Type. Transl. Math. Monogr.,23, Amer. Math. Soc., Providence, R. I. 1968.

    Google Scholar 

  9. H. Matano, Nonincrease of the lap-number of a solution for a one-dimensional semilinear parabolic equation. J. Fac. Sci. Univ. Tokyo, Sect. IA, Math.,29 (1982), 401–441.

    MATH  MathSciNet  Google Scholar 

  10. T. Nagai and M. Mimura, Some nonlinear degenerate diffusion equation related to population dynamics. J. Math. Soc. Japan.,35 (1983), 539–562.

    Article  MATH  MathSciNet  Google Scholar 

  11. T. Nagai and M. Mimura, Asymptotic behavior for a nonlinear degenerate diffusion equation in population dynamics. SIAM J. Appl. Math.,43 (1983), 449–464.

    Article  MATH  MathSciNet  Google Scholar 

  12. J. L. Vázquez, Asymptotic behaviour and propagation properties of the one-dimensional flow of gas in a porous medium. Trans. Amer. Math. Soc.,277 (1983), 507–527.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Education, Ehime University, 790, Ehime, Japan

    Toshitaka Nagai

  2. Department of Mathematics, Hiroshima University, 730, Hiroshima, Japan

    Masayasu Mimura

Authors
  1. Toshitaka Nagai
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  2. Masayasu Mimura
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Nagai, T., Mimura, M. Asymptotic Behavior of the interfaces to a nonlinear degenerate diffusion equation in population dynamics. Japan J. Appl. Math. 3, 129–161 (1986). https://doi.org/10.1007/BF03167095

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  • DOI: https://doi.org/10.1007/BF03167095

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