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

doi:10.1007/s10473-024-0420-8

摘要/Abstract

摘要： 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.

关键词: degenerate diffusion, $p$-Laplacian, traveling waves, stability

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

中图分类号:

35K57

Rui Huang, Yong Wang, Zhuo Yin. ON MONOTONE TRAVELING WAVES FOR NICHOLSON'S BLOWFLIES EQUATION WITH DEGENERATE $p$-LAPLACIAN DIFFUSION[J]. 数学物理学报(英文版), 2024, 44(4): 1550-1571.

Rui Huang, Yong Wang, Zhuo Yin. ON MONOTONE TRAVELING WAVES FOR NICHOLSON'S BLOWFLIES EQUATION WITH DEGENERATE $p$-LAPLACIAN DIFFUSION[J]. Acta mathematica scientia,Series B, 2024, 44(4): 1550-1571.

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