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Spreading Speed in A Nonmonotone Equation with Dispersal and Delay

Author

Listed:
  • Xi-Lan Liu

    (School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shannxi, China)

  • Shuxia Pan

    (School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China)

Abstract

This paper is concerned with the estimation of spreading speed of a nonmonotone equation, which involves time delay and nonlocal dispersal. Due to the time delay, this equation does not generate monotone semiflows when the positive initial value is given. By constructing an auxiliary monotone equation, we obtain the spreading speed when the initial value admits nonempty compact support. Moreover, by passing to a limit function, we confirm the existence of traveling wave solutions if the wave speed equals to the spreading speed, which states the minimal wave speed of traveling wave solutions and improves the known results.

Suggested Citation

  • Xi-Lan Liu & Shuxia Pan, 2019. "Spreading Speed in A Nonmonotone Equation with Dispersal and Delay," Mathematics, MDPI, vol. 7(3), pages 1-9, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:291-:d:216054
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    Citations

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    Cited by:

    1. Luping Li & Shugui Kang & Lili Kong & Huiqin Chen, 2019. "Minimal Wave Speed in a Competitive Integrodifference System without Comparison Principle," Mathematics, MDPI, vol. 7(7), pages 1-11, June.
    2. Jorge E. Macías-Díaz & Nauman Ahmed & Muhammad Rafiq, 2019. "Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model," Mathematics, MDPI, vol. 7(12), pages 1-16, December.

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