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<p>In this paper, we determine sharp rates of accelerating propagation for a class of nonlocal dispersal cooperative systems from the perspective of probability theory by tracking the level sets of solutions with compactly supported initial conditions. First, the fundamental solution is established. Then, by exploring a variety of tail asymptotic properties of multiple convolutions of nonlocal dispersal kernels with different decays, the fine estimates of the fundamental solution are captured from above and below, which play a key role in delicate construction of super- and sub-solutions. Finally, based on the evolutionary viewpoint and comparison arguments, sharp rates of accelerating propagation for nonlocal dispersal cooperative systems are determined.</p>

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Sharp rates of accelerating propagation for nonlocal dispersal cooperative systems

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Na Li

摘要

In this paper, we determine sharp rates of accelerating propagation for a class of nonlocal dispersal cooperative systems from the perspective of probability theory by tracking the level sets of solutions with compactly supported initial conditions. First, the fundamental solution is established. Then, by exploring a variety of tail asymptotic properties of multiple convolutions of nonlocal dispersal kernels with different decays, the fine estimates of the fundamental solution are captured from above and below, which play a key role in delicate construction of super- and sub-solutions. Finally, based on the evolutionary viewpoint and comparison arguments, sharp rates of accelerating propagation for nonlocal dispersal cooperative systems are determined.