Open Access$m$th-order Fisher-KPP equation with free boundaries and time-aperiodic advection
Author(s) -
Changqing Ji,
Dandan Zhu,
Jingli Ren
Publication year - 2021
Publication title -
mathematics in applied sciences and engineering
Language(s) - English
Resource type - Journals
ISSN - 2563-1926
DOI - 10.5206/mase/13996
Subject(s) - trichotomy (philosophy) , advection , aperiodic graph , amplitude , mathematics , term (time) , mathematical analysis , physics , optics , quantum mechanics , philosophy , linguistics , combinatorics
In this paper, we investigate a $m$th-order Fisher-KPP equation with free boundaries and time-aperiodic advection. Considering the influence of advection term and initial conditions on the long time behavior of solutions, we obtain spreading-vanishing dichotomy, spreading-transition-vanishing trichotomy, and vanishing happens with the coefficient of advection term in small amplitude, medium-sized amplitude and large amplitude, respectively. Then, the appropriate parameters are selected in the simulation to intuitively show the corresponding theoretical results. Moreover, the wave-spreading and wave-vanishing cases of the solutions are observed in our study.