Spreading Speed in A Nonmonotone Equation with Dispersal and Delay

Mathematics

Xi-Lan Liu¹  Shuxia Pan² 

[1] School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shannxi, China;School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China;

关键词: asymptotic spreading;    auxiliary equation;    minimal wave speed;   

DOI  :  10.3390/math7030291

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown