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<p>In this paper, spreading properties of reaction-diffusion systems with cooperative and reducible nonlinearity are considered. Weinberger et al. [J. Math. Biol. <b>45</b> (2002) 183-218] demonstrated that components of reducible cooperative systems can spread at distinct finite speeds for given compactly supported initial conditions. We extend this analysis by considering the possible acceleration spreading. Our findings reveal that all components can propagate at different speeds, either linearly or superlinearly (acceleration). By employing the graph theory, we specifically characterize the level sets of solutions, illustrating the influence of the cooperative effect. Examples are presented to illustrate the obtained results.</p>

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Fast propagation in cooperative reducible reaction-diffusion systems

  • 期刊论文

  • 发表日期：

    2025年12月4日

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  • Biao Liu,
  • Wan-Tong Li,
  • Guo Lin,
  • Shigui Ruan

摘要

In this paper, spreading properties of reaction-diffusion systems with cooperative and reducible nonlinearity are considered. Weinberger et al. [J. Math. Biol. 45 (2002) 183-218] demonstrated that components of reducible cooperative systems can spread at distinct finite speeds for given compactly supported initial conditions. We extend this analysis by considering the possible acceleration spreading. Our findings reveal that all components can propagate at different speeds, either linearly or superlinearly (acceleration). By employing the graph theory, we specifically characterize the level sets of solutions, illustrating the influence of the cooperative effect. Examples are presented to illustrate the obtained results.