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Mathematics 2019, 7(3), 291; https://doi.org/10.3390/math7030291

Spreading Speed in A Nonmonotone Equation with Dispersal and Delay

1
School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shannxi, China
2
School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China
*
Author to whom correspondence should be addressed.
Received: 27 February 2019 / Revised: 15 March 2019 / Accepted: 18 March 2019 / Published: 21 March 2019
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PDF [728 KB, uploaded 21 March 2019]

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. View Full-Text
Keywords: asymptotic spreading; auxiliary equation; minimal wave speed asymptotic spreading; auxiliary equation; minimal wave speed
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Liu, X.-L.; Pan, S. Spreading Speed in A Nonmonotone Equation with Dispersal and Delay. Mathematics 2019, 7, 291.

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