Generalized traveling waves for time-dependent reaction–diffusion systems
Generalized traveling waves for time-dependent reaction–diffusion systems
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DOI：
10.1007/s00208-020-01998-3
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发表时间：
2020-04
影响因子：
1.4
通讯作者：
B. Ambrosio;A. Ducrot;S. Ruan
中科院分区：
文献类型：
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作者：
B. Ambrosio;A. Ducrot;S. Ruan
一般含时（包括周期）反应扩散方程和方程组的行波解在过去的二十年里引起了人们的极大关注。本文的目的是研究一般的时间异构环境中的传播现象。更具体地说，我们研究了两个组件的时间依赖的非合作反应扩散系统，在流行病学和生态学的应用广义行波解。建立了广义行波解存在和不存在的充分条件。在非传染性流行病模型中，广义行波描述了疾病在时空上对完全易感人群的侵袭。在捕食-食饵系统中，广义行波描述了捕食者的空间入侵引入到一个新的环境中，食饵种群是在其承载能力。
Traveling wave solutions in general time-dependent (including time-periodic) reaction–diffusion equations and systems of equations have attracted great attention in the last two decades. The aim of this paper is to study the propagation phenomenon in a general time-heterogeneous environment. More specifically, we investigate generalized traveling wave solutions for a two-component time-dependent non-cooperative reaction–diffusion system which has applications in epidemiology and ecology. Sufficient conditions on the existence and nonexistence of generalized traveling wave solutions are established. In the susceptible-infectious epidemic model setting, generalized traveling waves describe the spatio-temporal invasion of a disease into a totally susceptible population. In the context of predator–prey systems, the generalized traveling waves describe the spatial invasion of predators introduced into a new environment where the prey population is at its carrying capacity.