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Existence and stability of travelling wave solutions of a nonlinear integral operator

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In this paper, we establish the existence and stability property of travelling wave solutions of a nonlinear integral operator in the inferior case.

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References

  1. Aronson, D. G., Weinberger, H. F.: Nonlinear diffusion in population genetics, combustion, and nerve propagation. In: Goldstein, J. (ed.) Partial differential equations and related topics. Lecture notes in mathematics, vol. 446, 5–49. Berlin-Heidelberg-New York: Springer 1975

    Google Scholar 

  2. Aronson, D. G., Weinberger, H. F.: Multidimensional nonlinear diffusion arising in population genetics. Adv. in Math. 30, 33–76 (1978)

    Google Scholar 

  3. Diekmann, O.: Thresholds and travelling waves for the geographical spread of infection. J. Math. Biol. 6, 109–130 (1978)

    Google Scholar 

  4. Diekmann, O.: Run for your life. A note on the asymptotic speed of propagation of an epidemic. J. Different. Equa. 33, 58–73 (1979)

    Google Scholar 

  5. Diekmann, O., Kaper, H. G.: On the bounded solutions of a nonlinear convolution equation. J. Nonlin. Analysis 2, 721–737 (1978)

    Google Scholar 

  6. Fife, P. C., McLeod, J. B.: The approach of solutions of nonlinear diffusion equations to travelling wave solutions. Arch. for Rat. Mech. and Anal. 65, 335–361 (1977)

    Google Scholar 

  7. Hadeler, K. P., Rothe, F.: Travelling fronts in nonlinear diffusion equations. J. Math. Biol. 2, 251–263 (1975)

    Google Scholar 

  8. Thieme, H. R.: Asymptotic estimates of the solutions of nonlinear integral equations and the asymptotic speeds for the spread of populations. J. Reine und Angew. Math. 306, 94–121 (1979)

    Google Scholar 

  9. Thieme, H. R.: Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread. J. Math. Biol. 8, 173–187 (1979)

    Google Scholar 

  10. Lui, R.: A nonlinear integral operator arising from a model in population genetics I. Monotone initial data. SIAM J. on Math. Analysis, in press (1982)

  11. Lui, R.: A nonlinear integral operator arising from a model in population genetics II. Initial data with compact support. SIAM J. on Math. Analysis, in press (1982)

  12. Schumacher, K.: Travelling-front solutions for integro-differential equations I. J. Reine und Angew. Mathematik 316, 54–70 (1980)

    Google Scholar 

  13. Schumacher, K.: Travelling-front solutions for integro-differential equations II. Biological growth and spread, mathematical theory, and applications. Proceedings Heidelberg 1979. Lecture notes in biomathematics, vol. 38. Berlin-Heidelberg-New York: Springer 1979

    Google Scholar 

  14. Veling, E. J. M.: Convergence to a travelling wave in an initial-boundary value problem, ordinary and partial differential equations. Proceedings Dundee Scotland 1980. Lecture notes in mathematics, vol. 846. Berlin-Heidelberg-New York: Springer 1980

    Google Scholar 

  15. Weinberger, H. F.: Asymptotic behavior of a model in population genetics. In: Chadam, J. (ed.) Nonlinear partial differential equations and applications. Lecture notes in math., vol. 648, 47–98. Berlin-Heidelberg-New York: Springer 1978

    Google Scholar 

  16. Weinberger, H. F.: Long-time behavior of a class of biological models. SIAM J. on Math. Analysis 13, (No. 3) 353–396 (1982)

    Google Scholar 

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Lui, R. Existence and stability of travelling wave solutions of a nonlinear integral operator. J. Math. Biology 16, 199–220 (1983). https://doi.org/10.1007/BF00276502

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