Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (4): 1550-1571.doi: 10.1007/s10473-024-0420-8

Previous Articles     Next Articles

ON MONOTONE TRAVELING WAVES FOR NICHOLSON'S BLOWFLIES EQUATION WITH DEGENERATE $p$-LAPLACIAN DIFFUSION

Rui Huang, Yong Wang*, Zhuo Yin   

  1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • Received:2023-06-15 Online:2024-08-25 Published:2024-08-30
  • Contact: *E-mail: wangyongxmu@163.com
  • About author:E-mail: huangrui@m.scnu.edu.cn; YinZhuoMAX@163.com
  • Supported by:
    Huang's work was partially supported by the NSFC (11971179, 12371205); Wang's work was partially supported by the National Key R&D Program of China (2021YFA1002900), the Guangdong Province Basic and Applied Basic Research Fund (2021A1515010235) and the Guangzhou City Basic and Applied Basic Research Fund (2024A04J6336).

Abstract: We study the existence and stability of monotone traveling wave solutions of Nicholson's blowflies equation with degenerate $p$-Laplacian diffusion. We prove the existence and nonexistence of non-decreasing smooth traveling wave solutions by phase plane analysis methods. Moreover, we show the existence and regularity of an original solution via a compactness analysis. Finally, we prove the stability and exponential convergence rate of traveling waves by an approximated weighted energy method.

Key words: degenerate diffusion, $p$-Laplacian, traveling waves, stability

CLC Number: 

  • 35K57
Trendmd